📚 Mind Map Quick Revision for Edexcel A-Level Physics | 思维导图速记 A-Level Edexcel 物理
Unlock the full potential of your Edexcel A-Level Physics revision with mind maps — a visual tool that transforms complex topics into clear, interconnected ideas. This guide will show you how to build effective mind maps tailored to the Edexcel specification, helping you memorise key concepts, formulae, and practical skills faster and more systematically.
Physics is not just a collection of isolated facts; it is a web of linked principles. Mind maps mirror this structure by showing relationships between topics like forces, energy, and fields. This visual layout activates both sides of your brain, improving recall and understanding compared to linear notes.
For Edexcel A-Level, the syllabus covers topics from mechanics to nuclear physics, and many questions require you to synthesise knowledge from different areas. A well‑designed mind map lets you see these connections at a glance, making it easier to tackle synoptic questions in Paper 1 and Paper 2.
Start by creating a master mind map with the main branches of Edexcel Physics: Mechanics, Electric Circuits, Materials, Waves and Particle Nature of Light, Thermodynamics, Nuclear and Particle Physics, and Fields. Each branch will then have sub‑topics such as SUVAT equations, Ohm’s Law, Young’s modulus, interference, ideal gases, and binding energy.
Keep this overview map on your wall or as your desktop background. It serves as a roadmap, showing you exactly how far you have come in your revision and what still needs attention.
把这张总览图贴在墙上或设为桌面背景。它就像一幅路线图，时刻提醒你复习的进度以及尚未攻克的部分。
3. Mechanics Mind Map | 力学思维导图
Mechanics is the foundation of A-Level Physics. Begin with vectors and scalars in the centre, then branch out to kinematics (suvat), dynamics (Newton’s laws), energy, momentum, and moments. For each sub‑topic, add the key equation in a bold colour, for example F = m a, E = ½ m v², and p = m v.
力学是 A-Level 物理的根基。以矢量和标量为中心，然后向外展开运动学（匀加速方程）、动力学（牛顿定律）、能量、动量和力矩。在每个子主题旁边，用醒目的颜色标注关键方程，例如 F = m a、E = ½ m v² 和 p = m v。
Link the conservation laws together: conservation of energy connects to work done, and conservation of momentum connects to impulse and collisions. Add a branch for circular motion, highlighting the centripetal force F = m ω² r and the conditions for uniform circular motion. Don’t forget oscillations from simple harmonic motion, where a = – ω² x, a direct link to mechanics and waves.
把守恒定律联系起来：能量守恒连接做功，动量守恒连接冲量和碰撞。再增加一个圆周运动分支，突出向心力 F = m ω² r 和匀速圆周运动的条件。别忘了简谐运动中的振动，其 a = – ω² x 是力学与波的直接桥梁。
SUVAT: v = u + at
s = ut + ½ at²
Newton II: F = ma
Momentum: p = mv
Kinetic Energy: ½ mv²
Spring Energy: ½ k Δx²
4. Electric Circuits Mind Map | 电路思维导图
Electricity is often perceived as abstract, but a mind map can make the flow of charge tangible. Start with current, potential difference, and resistance, then derive Ohm’s Law V = I R. Branch into series and parallel rules: current splits, voltage splits, resistances add differently. Include the internal resistance of a cell and the terminal pd equation V = E – I r.
电学常被认为抽象，但思维导图能让电荷的流动变得具体。从电流、电势差和电阻开始，进而推导出欧姆定律 V = I R。接着分支到串联和并联的规则：电流如何分配、电压如何分配、电阻如何计算。别忘了电源内阻和端电压方程 V = E – I r。
Add a sub‑branch for resistivity R = ρ l / A and the experimental determination of resistivity. Connect the concept of power P = I V, P = I² R, P = V² / R to the heating effect and energy transfer. For potential dividers, draw a quick sketch on your mind map to show how the output voltage varies with a variable resistor or sensor.
增加一个关于电阻率 R = ρ l / A 的子分支，并记下电阻率测定的实验方法。将功率 P = I V、P = I² R、P = V² / R 与热效应和能量转换联系起来。对于分压器，可在思维导图上草画一图，展示输出电压如何随可变电阻或传感器变化。
5. Materials Mind Map | 材料力学思维导图
Materials physics links macroscopic behaviour to microscopic structure. The central concept is stress and strain. Place Hooke’s Law (F = k Δx) and the Young modulus (E = stress / strain) at the core. Then branch out to elastic and plastic deformation, with descriptions of the force‑extension graph features such as the limit of proportionality and elastic limit.
材料物理将宏观行为与微观结构联系起来。核心概念是应力和应变。把胡克定律（F = k Δx）和杨氏模量（E = stress / strain）放在中心。然后分支到弹性形变和塑性形变，并描述力‑延伸图的关键特征，比如比例极限和弹性极限。
Include a branch for stress‑strain curves of different materials: brittle (e.g. glass), ductile (e.g. copper), and polymeric (e.g. rubber). Label the area under the curve as strain energy per unit volume. The energy stored = ½ F Δx for elastic deformation. Finally, link this to springs in series and parallel, as they often appear in exam questions.
增加不同材料应力‑应变曲线的分支：脆性材料（如玻璃）、延性材料（如铜）和高分子材料（如橡胶）。在曲线下方标注其面积为单位体积的应变能。弹性形变时储存的能量为 ½ F Δx。最后，将其与弹簧的串联和并联连接起来，这是考试中的常见题型。
6. Waves and Light Mind Map | 波与光思维导图
Waves appear in both mechanical and electromagnetic contexts. Start with the wave equation v = f λ. Distinguish transverse and longitudinal waves with clear diagrams. Superposition and interference are central: path difference, phase difference, and the conditions for constructive (path diff = n λ) and destructive interference.
波既包括机械波也包括电磁波。从波速方程 v = f λ 开始。用清晰的图示区分横波和纵波。叠加和干涉是核心：路程差、相位差，以及相长干涉（路程差 = n λ）和相消干涉的条件。
For light, create a branch for Young’s double‑slit experiment: λ = a x / D, where a is slit separation. Diffraction gratings use d sinθ = n λ. Connect these to the wave nature of light and the electromagnetic spectrum. Then add stationary waves on strings and in pipes, with the harmonic frequency formulas: f = n v / (2L) for open pipes, f = (2n‑1) v / (4L) for closed pipes.
对于光，建立杨氏双缝干涉分支：λ = a x / D，其中 a 为缝间距。衍射光栅使用 d sinθ = n λ。把这些与光的波动性和电磁波谱联系起来。然后添加弦上和管内驻波的内容，以及谐波频率公式：开管 f = n v / (2L)，闭管 f = (2n‑1) v / (4L)。
7. Quantum and Particle Physics Mind Map | 量子与粒子物理思维导图
This topic challenges classical intuition, but a mind map can structure the key experiments and their interpretations. Start with the photoelectric effect: Einstein’s equation hf = Φ + ½ m v²max. Show how the Gold leaf electroscope and vacuum photocell experiments demonstrate the particle nature of light.
这个主题挑战经典直觉，但思维导图能帮你梳理关键实验及其物理诠释。从光电效应开始：爱因斯坦方程 hf = Φ + ½ m v²max。展示金箔验电器和真空光电管实验如何证明光的粒子性。
Branch into atomic structure: Rutherford scattering, nuclear model, energy levels, and emission/absorption spectra. Use E = h f = h c / λ and the idea of quantised energy levels ΔE = h f. For particle physics, map out the standard model with quarks, leptons, and gauge bosons. Keep the conservation laws (charge, baryon number, lepton number) as a central checklist for analysing interactions.
分支到原子结构：卢瑟福散射、核式模型、能级以及发射/吸收光谱。运用 E = h f = h c / λ 和量子化能级 ΔE = h f 的概念。对于粒子物理，用思维导图整理标准模型，包括夸克、轻子和规范玻色子。将守恒律（电荷数、重子数、轻子数）作为分析相互作用的中心核对清单。
8. Thermodynamics Mind Map | 热力学思维导图
Thermal physics connects macroscopic properties (pressure, volume, temperature) with microscopic particle behaviour. The ideal gas equation p V = n R T and the kinetic theory equation p V = 1/3 N m are central. Use a mind map to link them, showing how 1/2 m = 3/2 k T.
热物理将宏观性质（压强、体积、温度）与微观粒子行为联系起来。理想气体状态方程 p V = n R T 和分子动理论方程 p V = 1/3 N m 是中心内容。用思维导图将它们连接起来，展示如何得出 1/2 m = 3/2 k T。
Add a branch for the first law of thermodynamics ΔU = Q – W, explaining the sign convention for work done by the gas. Connect this to isothermal, adiabatic, and constant‑pressure processes, with p‑V diagrams. The efficiency of heat engines and the concept of entropy can be added as advanced extensions.
增加热力学第一定律 ΔU = Q – W 的分支，解释气体做功的符号惯例。将其与等温、绝热、等压过程以及 p‑V 图联系起来。热机效率和熵的概念可以作为进阶补充内容加入导图。
9. Fields Mind Map | 场思维导图
Fields are a unifying theme in advanced physics. Begin with gravitational fields: g = F / m, field lines, and F = G M m / r². Distinguish between uniform (parallel lines) and radial fields. Then create a parallel branch for electric fields: E = F / Q, F = k Q q / r², and E = V / d for a uniform field.
场是高等物理中一个统领全局的主题。从引力场开始：g = F / m，力线以及 F = G M m / r²。区分均匀场（平行线）和辐射状场。然后建立电场的平行分支：E = F / Q、F = k Q q / r² 以及均匀场中的 E = V / d。
Connect to potential V and potential energy. For gravity, V = – G M / r and escape velocity. For electricity, V = k Q / r and the motion of charged particles in electric fields. Add magnetic fields with F = B I l sinθ and F = B q v sinθ for moving charges. Link this to electromagnetic induction: Faraday’s law ε = – N ΔΦ / Δt and Lenz’s law. The cross‑linkages between gravitational, electric, and magnetic fields are excellent for a mind map.
将场与势 V 和势能连接起来。对于引力场，V = – G M / r 和逃逸速度。对于电场，V = k Q / r 以及带电粒子在电场中的运动。再添加磁场内容，包括 F = B I l sinθ 和运动电荷的 F = B q v sinθ。将此与电磁感应联系起来：法拉第定律 ε = – N ΔΦ / Δt 和楞次定律。引力场、电场和磁场之间的交叉联系非常适合用思维导图来呈现。
10. Practical Skills and Data Analysis | 实验技能与数据分析
Paper 3 and the practical endorsement require solid experimental techniques. Create a mind map for common practicals: determination of g by free fall, measurement of the resistivity of a wire, investigation of a capacitor discharge, and the Young double‑slit experiment. For each, note the key measurements, derived quantities, and major sources of uncertainty.
Add a branch for data analysis: combining uncertainties (absolute, fractional, percentage), plotting graphs (line of best fit, error bars), and interpreting logarithmic plots. Include the formula for gradient uncertainty. Also highlight how to use a micrometer, vernier caliper, oscilloscope, and multimeter. These practical links remind you that theory and experiment are inseparable in Edexcel Physics.
Effective mind maps are personal. Start with a blank sheet of paper (or digital tool) and put the topic name in the centre. Use branches radiating outward, each in a different colour. Write key words, not long sentences. Draw small, memorable symbols next to physical quantities: a snowflake for absolute zero, a lightning bolt for voltage, a sine curve for waves.
After drawing the first version, revisit it after solving past paper questions. Add annotations: common pitfalls, exam keywords that trigger certain equations, and alternative definitions. Over time, your mind map becomes a living summary that grows with your understanding. Swap maps with a study partner to gain new perspectives.
Use active recall: cover a branch and try to reproduce it from memory. Then check against your original. Teach a friend from your map without looking at extra notes. Spaced repetition: review your maps at increasing intervals — 1 day, 3 days, 1 week, 1 month.
Integrate mind maps with the Edexcel specification checklist. Tick off each point as you can recall its position and content on your map. This transforms a dry list into a vivid mental journey. After all, the brain remembers images and connections far better than isolated text.
📚 IB Physics: Mind Map Quick Recall | IB 物理：思维导图速记
IB Physics demands the assimilation of a vast array of concepts, equations, and experimental techniques across multiple topics. A mind map transforms this dense syllabus into a visual, interconnected network of ideas, making it far easier to memorise and retrieve during exams. By structuring knowledge around central themes and branching out with concise cues, you can quickly recall entire topic areas.
1. Mind Mapping Fundamentals for IB Physics | IB 物理思维导图基础
Place the core subject ‘IB Physics’ at the centre of your page. From it, radiate eight main topic branches corresponding to the Standard Level syllabus. Use colour coding for each branch, draw simple icons for key quantities (e.g., a spring for force, a battery for electricity), and limit each node to one or two keywords. The goal is to create a single-page overview that triggers detailed knowledge stored in your long-term memory.
When revising, cover parts of the map and test yourself on the links and formulas. Over time, your brain will associate the visual layout with the underlying physics, enabling lightning-fast recall in the exam hall.
Begin your ‘Measurements & Uncertainties’ branch with a sub-node for Fundamental SI Units. The seven base units are kilogram (kg), metre (m), second (s), ampere (A), mole (mol), kelvin (K) and candela (cd). All other units in physics are derived from these.
Add a sub-branch for Uncertainties and Significant Figures. For a digital instrument, the absolute uncertainty is half the smallest scale division; for an analogue instrument, it is the smallest division. Fractional uncertainty is the absolute uncertainty divided by the measured value, while percentage uncertainty multiplies this by 100%.
Vectors and scalars are essential. Represent vector addition and subtraction using tip-to-tail diagrams. Trigonometry helps resolve vectors into perpendicular components.
矢量与标量至关重要。使用首尾相连的图示来表示矢量的加减。三角函数有助于将矢量分解为垂直分量。
Absolute uncertainty = ½ × smallest scale division (digital) or 1 division (analogue)
Draw the ‘Mechanics’ main branch and split it into Kinematics, Forces, Work, Energy & Power, and Momentum & Impulse. For kinematics, the ‘SUVAT’ equations are the core: link them to the conditions of constant acceleration in a straight line.
v = u + a t ; s = u t + ½ a t² ; v² = u² + 2 a s ; s = ½ (u + v) t
In the Forces sub-branch, Newton’s three laws govern motion. Connect free-body diagrams with the equation F = m a. Remember that friction opposes relative motion, and tension is constant in a light inextensible string.
在“力”子分支中，牛顿三大定律主导运动。将受力分析图与方程 F = m a 联系起来。记住摩擦力阻碍相对运动，轻质不可伸长绳中的张力处处相等。
For Work, Energy & Power, highlight the work-energy theorem and the conservation of mechanical energy only when no non-conservative forces act. Kinetic energy Eₖ = ½ m v², gravitational potential energy Eₚ = m g h, and power P = W / t = F v.
在“功、能量与功率”子分支中，强调功能原理以及仅在无非保守力做功时机械能守恒。动能 Eₖ = ½ m v²，重力势能 Eₚ = m g h，功率 P = W / t = F v。
The momentum branch links impulse to change in momentum: F Δt = Δp = m(v – u). The principle of conservation of momentum is crucial for collisions and explosions, especially in two dimensions.
Eₖ = ½ m v² ; Eₚ = m g h ; p = m v ; Impulse = F Δt = Δp
4. Thermal Physics | 热学
The thermal physics branch revolves around temperature, heat transfer, and the gas laws. Define temperature in terms of the average random kinetic energy of particles. Distinguish between thermal energy and temperature clearly in your mind map.
Use a sub-branch for Specific and Latent Heats. When a substance changes temperature, Q = m c ΔT. During a phase change at constant temperature, Q = m L, where L is the specific latent heat (fusion or vaporisation).
使用一个子分支代表比热容与潜热。物质温度变化时，Q = m c ΔT；在等温相变过程中，Q = m L，其中 L 为比潜热（熔解热或汽化热）。
The ideal gas laws unify pressure, volume, and temperature: p V = n R T, where n is the number of moles. For a fixed mass, p V / T = constant. Interpret the kinetic model via p V = (1/3) N m c²rms.
理想气体定律统一了压强、体积和温度：p V = n R T，其中 n 为摩尔数。对于一定质量的气体，p V / T = 常数。通过 p V = (1/3) N m c²rms 理解分子的动力学模型。
Q = m c ΔT ; Q = m L ; p V = n R T ; p V / T = constant
Average kinetic energy per molecule ∝ T
5. Waves | 波
The waves branch starts with the difference between transverse and longitudinal oscillations. Identify examples: light and water waves are transverse; sound is longitudinal. The universal wave equation v = f λ links speed, frequency, and wavelength.
波的分支从横波与纵波的差异开始。识别例子：光和水波是横波；声波是纵波。普适波动方程 v = f λ 将波速、频率和波长连接起来。
Label a sub-branch for Wavefronts and Rays. Describe reflection, refraction, diffraction, and superposition. Emphasis on Snell’s law: n₁ sin θ₁ = n₂ sin θ₂, where n = c / v is the absolute refractive index.
标注一个关于波前与射线的子分支。描述反射、折射、衍射和叠加。重点放在斯涅尔定律：n₁ sin θ₁ = n₂ sin θ₂，其中 n = c / v 为绝对折射率。
For standing waves, note the patterns of nodes (zero displacement) and antinodes (maximum displacement) on strings and in pipes. Standing wave harmonics form only at specific frequencies: for a string fixed at both ends, fₙ = n v / (2L).
对于驻波，注意弦和管中波节（位移为零）和波腹（位移最大）的图样。驻波谐波只在特定频率形成：两端固定的弦上，fₙ = n v / (2L)。
Do not forget single-slit diffraction and the condition for minima: a sin θ = n λ. This links the wave nature of light to the slit width a.
别忘了单缝衍射及其极小条件：a sin θ = n λ。这联系了光的波动本性与缝宽 a。
v = f λ ; n = c / v ; n₁ sin θ₁ = n₂ sin θ₂
String fixed at both ends: fₙ = n v / (2L) ; Single slit minimum: a sin θ = n λ
6. Electricity and Magnetism | 电磁学
In your electricity sub-branch, start with charge, current, and potential difference. Define current I = Δq / Δt and use Ohm’s law V = I R for ohmic conductors. Resistance depends on resistivity, length, and cross-sectional area: R = ρ L / A.
在电学子分支中，从电荷、电流和电势差开始。定义电流 I = Δq / Δt，对欧姆导体使用欧姆定律 V = I R。电阻取决于电阻率、长度和横截面积：R = ρ L / A。
Branch out to circuit diagrams: series resistors add (R_total = R₁ + R₂ + …), while parallel resistors follow 1/R_total = 1/R₁ + 1/R₂ + … . Kirchhoff’s current law (junction rule) and voltage law (loop rule) govern complex circuits.
Under magnetism, learn the force on a current-carrying wire: F = B I L sin θ, where B is magnetic flux density. The direction is given by Fleming’s left-hand rule. A moving charge in a magnetic field experiences a force F = q v B sin θ, leading to circular motion.
在磁学部分，学习通电导线所受的力：F = B I L sin θ，其中 B 为磁感应强度。方向由弗莱明左手定则给出。运动电荷在磁场中受到的力 F = q v B sin θ 会使其做圆周运动。
V = I R ; P = I V = I² R = V² / R ; R = ρ L / A
F = B I L sin θ ; F = q v B sin θ ; Series: R_total = Σ R ; Parallel: 1/R_total = Σ (1/R)
7. Circular Motion and Gravitation | 圆周运动与引力
For circular motion, distinguish between tangential velocity and angular velocity. The period T relates to angular speed ω via ω = 2π / T. Centripetal acceleration always points towards the centre: a = v² / r = ω² r.
对于圆周运动，区分线速度与角速度。周期 T 与角速度 ω 的关系为 ω = 2π / T。向心加速度始终指向圆心：a = v² / r = ω² r。
Centripetal force is the net force causing this acceleration, and it is not a separate force but the resultant of existing forces (tension, friction, gravity). For a car rounding a bend, friction provides the centripetal force.
Under gravitation, Newton’s law of universal gravitation states F = G M m / r². Gravitational field strength g = F / m = G M / r² near a spherical mass. Equate centripetal force with gravitational force to derive satellite orbital velocity v = √(G M / r).
在引力部分，牛顿万有引力定律表述为 F = G M m / r²。在球体质量附近，引力场强 g = F / m = G M / r²。令向心力等于引力，可推导出卫星的轨道速度 v = √(G M / r)。
v = ω r ; a = v² / r = ω² r ; F = m v² / r
F = G M m / r² ; g = G M / r² ; v_orbit = √(G M / r)
8. Atomic, Nuclear and Particle Physics | 原子、核与粒子物理
In this branch, map the structure of the atom: nucleus containing protons and neutrons, with electrons in discrete energy levels. Emphasise the photoelectric effect: the energy of a photon h f must exceed the work function Φ for electrons to be emitted. The maximum kinetic energy of photoelectrons is E_k,max = h f – Φ.
在这一分支中，描绘原子的结构：包含质子和中子的原子核，电子处于分立的能级。强调光电效应：光子能量 h f 必须超过逸出功 Φ 才能发射电子。光电子的最大动能为 E_k,max = h f – Φ。
Radioactive decay is described by the exponential law N = N₀ e^(–λ t), and the half-life t½ = ln 2 / λ. Know the types of radiation — alpha (⁴₂He), beta (e⁻ or e⁺), and gamma (electromagnetic) — and their penetrating abilities.
For nuclear reactions, recall mass-energy equivalence E = m c². The binding energy per nucleon curve explains both fission (heavy nuclei split) and fusion (light nuclei combine). Atomic masses are given in unified atomic mass units, u, where 1 u = 931.5 MeV c⁻².
对于核反应，记住质能等价 E = m c²。每个核子的结合能曲线解释了裂变（重核分裂）和聚变（轻核结合）。原子质量以统一原子质量单位 u 给出，1 u = 931.5 MeV c⁻²。
E = h f ; E_k,max = h f – Φ ; N = N₀ e^(–λ t) ; t½ = ln 2 / λ
E = m c² ; 1 u = 931.5 MeV / c²
9. Energy Production | 能源生产
The Energy Production branch links physics concepts to real-world power sources. Under fossil fuels, note the energy density and the production of carbon dioxide. Remember that a Sankey diagram visualises energy transformations and efficiency: efficiency = (useful power output) / (total power input).
Renewables like solar, wind, and hydroelectric have different advantages and limitations. Photovoltaic cells convert solar energy directly into electricity, while wind turbines convert kinetic energy of air. In all energy chains, describe the primary energy source and the generator principle of electromagnetic induction.
Nuclear power stations use controlled fission to heat a coolant and drive a turbine. The black-body radiation from the Sun peaks in the visible spectrum, and the solar constant is approximately 1361 W m⁻².
核电站利用受控裂变加热冷却剂，驱动涡轮。太阳黑体辐射的峰值位于可见光区，太阳常数约为 1361 W m⁻²。
Efficiency = P_out,useful / P_in,total ; Power = Energy / Time
10. HL Extension: Advanced Topics | 高级课程扩展：进阶专题
For Higher Level, extend your mind map with four extra branches. Wave Phenomena covers two-source interference, the double-slit formula s = λ D / d, thin-film interference, the Doppler effect for sound and light, and resolution limited by diffraction.
对于高级课程，在思维导图中增加四个额外分支。波动现象涵盖双源干涉、双缝公式 s = λ D / d、薄膜干涉、声和光的 Doppler 效应，以及受衍射所限的分辨率。
Fields include gravitational and electric potentials and fields. Gravitational potential V_g = –G M / r and electric potential V_e = k Q / r. Draw field lines and equipotential surfaces clearly. Link electric field strength to potential gradient: E = –ΔV / Δr.
场包含引力势与电势以及相应的场强。引力势 V_g = –G M / r，电势 V_e = k Q / r。清晰画出电场线与等势面。将电场强度与电势梯度联系起来：E = –ΔV / Δr。
Electromagnetic Induction emphasises Faraday’s law: ε = – N ΔΦ / Δt. Lenz’s law gives the direction of induced emf. Apply this to ac generators and transformers. Mutual inductance and self-inductance are governed by ε = – L dI/dt.
电磁感应强调法拉第定律：ε = – N ΔΦ / Δt。楞次定律给出了感生电动势的方向。将其应用于交流发电机和变压器。互感和自感由 ε = – L dI/dt 支配。
Quantum and Nuclear Physics deepens the photoelectric effect with the concept of photon momentum. The de Broglie wavelength λ = h / p exemplifies wave–particle duality. The uncertainty principle Δx Δp ≥ h/(4π) imposes fundamental limits. In nuclear physics, calculate mass defect and binding energy, and analyse radioactive decay series.
量子与核物理深化光电效应，引入光子动量概念。德布罗意波长 λ = h / p 体现了波粒二象性。不确定性原理 Δx Δp ≥ h/(4π) 给出了基本限制。在核物理中，计算质量亏损和结合能，并分析放射性衰变系。
Newton’s laws of motion form the foundation of classical mechanics and are central to the IGCSE AQA Physics syllabus. Students must not only recall the three laws but also apply them to explain everyday phenomena, calculate forces and accelerations, and interpret free-body diagrams. This article breaks down every key concept, provides clear definitions, highlights common pitfalls, and uses paired English-Chinese explanations to support bilingual learners aiming for high marks.
Newton’s first law states that an object will remain at rest or continue to move with constant velocity unless acted upon by a resultant (net) external force.
牛顿第一定律指出，除非受到合外力作用，物体将保持静止或匀速直线运动状态。
This tendency of an object to resist changes in its state of motion is called inertia. Inertia is directly related to mass: the greater the mass, the greater the inertia. For example, a loaded lorry has more inertia than a bicycle, so it is much harder to accelerate or decelerate.
On the IGCSE exam, you may be asked to explain why a passenger lurches forward when a bus brakes suddenly. The answer uses the first law: the passenger’s body continues moving forward at the original speed due to inertia while the bus decelerates.
When the forces acting on an object are balanced, the resultant force is zero. According to Newton’s first law, the object either stays at rest or keeps moving at constant speed in a straight line.
当作用在物体上的力相互平衡时，合力为零。根据牛顿第一定律，物体会保持静止或沿直线匀速运动。
When forces are unbalanced, there is a resultant force in a particular direction, causing the object to accelerate in that direction. It is crucial to remember that ‘accelerate’ means any change in velocity: speeding up, slowing down, or changing direction.
To find the resultant force, add all forces acting along the same line, taking direction into account. For perpendicular forces, use vector addition (though calculations at IGCSE often involve forces along a straight line).
This equation tells us that acceleration is directly proportional to the resultant force and inversely proportional to mass. A larger force gives a larger acceleration; a larger mass gives a smaller acceleration for the same force.
When using Fₙₑₜ = m a in IGCSE problems, always identify the resultant force first. Do not just plug in any given force — if there is friction or drag, you must subtract it.
在 IGCSE 题目中使用 Fₙₑₜ = m a 时，务必先确定合力。不要随便代入题目给出的某个力——如果有摩擦力或阻力，必须先减去。
4. The Newton as a Derived Unit | 导出单位牛顿
One newton is defined as the force that gives a mass of 1 kg an acceleration of 1 m/s². From F=ma, we obtain the unit equivalence:
1 牛顿的定义是使 1 kg 质量产生 1 m/s² 加速度所需的力。由 F=ma 可得出单位关系：
1 N = 1 kg m/s²
This derived unit is frequently tested. Be prepared to convert between N, kg, and m/s². Also, when using weight, remember that weight is a force measured in newtons, not kilograms.
Weight is the gravitational force exerted on an object by a planet. It is calculated by:
重力是行星对物体施加的引力，计算公式为：
W = m g
where W is weight (N), m is mass (kg), and g is the gravitational field strength (N/kg). On Earth, g ≈ 9.8 N/kg, but the exam often uses 10 N/kg for simplicity.
其中 W 是重力 (N)，m 是质量 (kg)，g 是引力场强度 (N/kg)。地球上 g ≈ 9.8 N/kg，但考试为简化常取 10 N/kg。
A common misconception is confusing mass with weight. Mass is the amount of matter in an object and does not change with location; weight depends on g and is smaller on the Moon. Always use W=mg to interconvert them.
In free fall, an object still has weight acting on it, but if the only force is weight, the acceleration is g. Exam questions often ask you to calculate weight, mass, or g.
6. Applying F=ma in Linear Motion | 直线运动中 F=ma 的应用
Typical IGCSE problems combine Newton’s second law with equations of motion. For instance, a car of mass 1200 kg experiences a resultant force of 3600 N. Find its acceleration.
典型的 IGCSE 题目将牛顿第二定律与运动学方程结合起来。例如，一辆质量为 1200 kg 的汽车受到 3600 N 的合力，求其加速度。
Using a = F / m = 3600 N / 1200 kg = 3.0 m/s².
使用 a = F / m = 3600 N / 1200 kg = 3.0 m/s²。
If friction or air resistance is given, subtract it from the driving force to obtain the resultant force before using F=ma. For example: driving force 5000 N, total resistive force 1400 N, mass 900 kg. Resultant force = 5000 N − 1400 N = 3600 N, then a = 3600/900 = 4.0 m/s².
若给出了摩擦或空气阻力，应在使用 F=ma 之前从驱动力中减去它们以得到合力。例如：驱动力 5000 N，总阻力 1400 N，质量 900 kg。合力 = 5000 N − 1400 N = 3600 N，则 a = 3600/900 = 4.0 m/s²。
Always show the resultant force step clearly in your working, as marks are awarded for the correct force value.
务必在解题步骤中清晰地展示合力计算过程，因为正确得出合力值就有分数。
7. Newton’s Third Law | 牛顿第三定律
Newton’s third law states: whenever two objects interact, they exert equal and opposite forces on each other. These forces are known as action-reaction pairs.
The key features of an action-reaction pair are: they act on two different objects, they are of the same type (e.g. both gravitational, both contact), and they are equal in magnitude and opposite in direction.
For example, when you push a wall, you exert a force on the wall, and the wall exerts an equal and opposite force on you. If you press a book down on a table, the book pushes down on the table, and the table pushes up on the book.
Do not confuse action-reaction pairs with equilibrium forces. Equilibrium forces act on the same object; third-law pairs act on different objects.
不要将作用力与反作用力对与平衡力混淆。平衡力作用在同一物体上；第三定律中的对作用在不同物体上。
8. Identifying Action-Reaction Pairs in Diagrams | 在示意图中识别作用力与反作用力对
IGCSE exam questions often show a simple scenario, such as a person standing on the ground or a rocket pushing exhaust gases backward, and ask you to identify the Newton’s third law pair.
For a person standing still: the Earth pulls the person down (weight), and the person pulls the Earth up with an equal gravitational force. Also, the ground pushes up on the person (normal contact force), and the person pushes down on the ground. Each is a third-law pair.
A rocket expels gas backwards; the rocket pushes the gas backwards, and the gas pushes the rocket forwards. This forward force is the thrust that accelerates the rocket in space where there is no air to push against.
To score full marks, always specify the two objects involved and the direction of each force.
要拿到满分，必须指明所涉及的两个物体以及每个力的方向。
9. Free Body Diagrams | 受力示意图
Free body diagrams (FBDs) simplify a situation by showing all the forces acting on a single object as arrows. The length of each arrow represents the magnitude, and the direction shows the direction of the force.
Common forces to include: weight (acting downwards from the centre of mass), normal reaction (perpendicular to the surface), tension (along a rope), friction (opposing motion), and applied forces.
When drawing FBDs for an accelerating object, the forces are not balanced; the resultant force points in the direction of acceleration. For an object at rest or moving at constant velocity, forces are balanced and arrows in opposite directions should have equal lengths.
AQA IGCSE questions may ask you to add force arrows to a diagram or explain the motion of an object from a given FBD. Practise drawing and interpreting them under exam conditions.
10. Common Misconceptions and Exam Tips | 常见误区与应试技巧
Misconception 1: ‘If there is no force, objects stop.’ This contradicts Newton’s first law. Objects stop only because of opposing forces like friction. In the absence of a resultant force, motion continues indefinitely.
Misconception 2: ‘Heavy objects fall faster.’ Without air resistance, all objects fall with the same acceleration g regardless of mass. This was famously demonstrated on the Moon.
Misconception 3: ‘Action and reaction cancel each other.’ They do not cancel because they act on different objects. Cancellation only occurs for forces on the same object.
Exam tip: Always analyse forces using the correct names (weight, normal force, friction, tension) and avoid vague terms like ‘moving force’. Use F=ma only after finding the resultant force. Show all steps clearly.
When a question asks ‘explain’, link your answer explicitly to a Newton law. For ‘calculate’, write the formula, substitute values, and state the unit. Pay attention to significant figures and unit conversions (e.g. grams to kilograms).
📚 Nuclear Physics Revision for IB & AQA | IB与AQA物理核物理考点精讲
Nuclear physics is a core topic for both IB and AQA A‑level Physics, covering the structure of the nucleus, radioactive decay, half‑life, mass–energy equivalence, nuclear binding energy, fission and fusion. This revision guide walks you through every essential concept, with worked examples and exam tips, to help you master the syllabus.
An atom consists of a tiny, dense nucleus containing nucleons (protons and neutrons), surrounded by electrons. The proton number (atomic number) Z determines the element, while the nucleon number (mass number) A gives the total number of nucleons. An isotope has the same Z but a different N = A – Z.
原子由一个极小、致密的原子核（内含质子和中子，统称核子）以及核外电子构成。质子数（原子序数）Z 决定元素种类，核子数（质量数）A 为总核子数。同位素具有相同的 Z 但不同的中子数 N = A – Z。
Proton mass ≈ 1.673 × 10⁻²⁷ kg, charge +e; neutron mass ≈ 1.675 × 10⁻²⁷ kg, no charge.
Radius of a nucleus R = R₀ A^(¹⁄³) with R₀ ≈ 1.2 fm. This shows that nuclear density is roughly constant for all nuclei.
原子核半径 R = R₀ A^(¹⁄³)，R₀ ≈ 1.2 fm。这表明所有核的核密度大致恒定。
Exam tip: convert between atomic mass units (1 u = 1.661 × 10⁻²⁷ kg) and energy (931.5 MeV) using E = mc².
考试提示：熟练运用原子质量单位（1 u = 1.661 × 10⁻²⁷ kg）与能量（931.5 MeV）的换算，利用 E = mc²。
2. The Strong Nuclear Force | 强核力
The strong nuclear force binds protons and neutrons together in the nucleus, overcoming the electrostatic repulsion between protons. It is a short‑range force that is attractive up to about 3 fm, repulsive at very short distances (< 0.5 fm), and negligible beyond 3 fm.
强核力将质子和中子束缚在原子核内，克服质子间的静电斥力。它是一种短程力：在约 3 fm 内表现为吸引，极短距离 (< 0.5 fm) 表现为排斥，超过 3 fm 可忽略。
It acts between all nucleons (p‑p, n‑n, p‑n) with the same strength.
强核力对任意核子对（p‑p、n‑n、p‑n）作用强度相同。
The stability of a nucleus depends on the balance between the strong force and Coulomb repulsion. Heavier nuclei need extra neutrons to provide more strong‑force binding without adding electrostatic repulsion.
核的稳定性取决于强力与库仑斥力的平衡。重核需要更多中子参与强相互作用而不增加静电斥力。
3. Radioactive Decay | 放射性衰变
An unstable nucleus spontaneously emits particles or electromagnetic radiation to become more stable. The three main types are alpha (α), beta (β) and gamma (γ) decay. The activity A of a sample is the number of decays per unit time, measured in becquerels (Bq), where 1 Bq = 1 decay per second.
Nature of emissions: α is a helium nucleus (²⁴He²⁺), β⁻ is an electron, β⁺ is a positron, γ is a high‑energy photon.
发射体本质：α 为氦核（²⁴He²⁺），β⁻ 为电子，β⁺ 为正电子，γ 为高能光子。
General decay equation for a parent nucleus X to daughter Y: A ᶻX → ᴬ⁻⁴ ᶻ⁻²Y + ²⁴α (α decay); A ᶻX → ᴬ ᶻ₊₁Y + e⁻ + ν̄ (β⁻ decay).
衰变通式：母核 X 变为子核 Y，α 衰变 A ᶻX → ᴬ⁻⁴ ᶻ⁻²Y + ²⁴α；β⁻ 衰变 A ᶻX → ᴬ ᶻ₊₁Y + e⁻ + ν̄。
4. Alpha Decay | α 衰变
Alpha decay occurs in heavy, neutron‑rich nuclei (Z > 82). An alpha particle is ejected, reducing the mass number by 4 and the atomic number by 2. The alpha particle has a discrete kinetic energy specific to the transition.
Alpha particles are highly ionising but have a very short range in matter (a few cm in air).
α 粒子电离本领强但穿透力弱，空气中射程仅几厘米。
5. Beta Decay | β 衰变
Beta decay is the emission of an electron (β⁻) or positron (β⁺) to change a neutron into a proton or a proton into a neutron, respectively, preserving the nucleon number but shifting Z by ±1. A neutrino or antineutrino is also emitted to conserve energy and momentum.
β⁻ decay: n → p + e⁻ + ν̄ₑ. Occurs in neutron‑rich nuclei.
β⁻ 衰变：n → p + e⁻ + ν̄ₑ，发生在富中子核。
β⁺ decay: p → n + e⁺ + νₑ. Occurs in proton‑rich nuclei.
β⁺ 衰变：p → n + e⁺ + νₑ，发生在富质子核。
Beta particles have a continuous spectrum of kinetic energies because the available energy is shared with the neutrino.
β 粒子动能谱连续，因为衰变能由电子和中微子共享。
6. Gamma Radiation | γ 辐射
Gamma radiation is an electromagnetic wave emitted when an excited nucleus moves to a lower energy state. Unlike α and β, gamma emission does not change A or Z; it simply releases excess energy.
γ 辐射是受激核跃迁至低能态时放出的电磁波。与 α、β 不同，γ 辐射不改变 A 或 Z，仅释放多余能量。
Gamma photons typically have energies in the MeV range and are highly penetrating, requiring lead or thick concrete for shielding.
γ 光子能量通常在 MeV 量级，穿透力强，需铅板或厚混凝土屏蔽。
Often follows an α or β decay, leaving the daughter nucleus in an excited state.
常伴随 α 或 β 衰变，子核处于激发态后放出 γ 退激。
7. The Decay Law and Half‑life | 衰变定律与半衰期
Radioactive decay is a random process described by the exponential decay law N = N₀ e^(−λt) and activity A = λN = A₀ e^(−λt), where λ is the decay constant (probability of decay per unit time).
放射性衰变是随机过程，遵循指数规律 N = N₀ e^(−λt)，活度 A = λN = A₀ e^(−λt)，λ 为衰变常量（单位时间衰变概率）。
N = N₀ e^(−λt) A = λN
Half‑life T₁/₂ is the time for half the original nuclei to decay: T₁/₂ = ln 2 / λ ≈ 0.693 / λ.
Examiners may ask you to find λ from a graph (gradient of ln N vs t is −λ) or to calculate remaining fraction after n half‑lives as (½)ⁿ.
考试中可能要求依据图像求 λ（ln N ‑ t 图斜率为 −λ），或计算 n 个半衰期后剩余分数为 (½)ⁿ。
8. Mass–Energy Equivalence | 质能等价
Einstein’s relation E = mc² links mass and energy. In nuclear processes, mass is not conserved, but the total mass–energy is conserved. A small change in mass Δm corresponds to a huge energy release or absorption: ΔE = Δm c².
爱因斯坦质能方程 E = mc² 建立了质量与能量联系。核过程中质量不守恒，但总质能守恒。微小的质量变化 Δm 对应巨大的能量释放或吸收：ΔE = Δm c²。
1 u of mass is equivalent to 931.5 MeV. Use this conversion in all mass‑defect calculations.
1 u 质量相当 931.5 MeV 能量。在所有质量亏损计算中需用此换算。
9. Nuclear Binding Energy | 核结合能
The binding energy of a nucleus is the energy required to separate it into its individual nucleons. It is equal to the mass defect Δm = (Zmₚ + Nmₙ) – M_nucleus, converted to energy using E = Δm c².
Binding energy per nucleon = total BE / A. This graph peaks at iron‑56, indicating the most stable nucleus.
平均结合能 = 总结合能 / A。该曲线在铁‑56 处最大，表明铁核最稳定。
Fusion (light nuclei) and fission (heavy nuclei) both move products towards higher binding energy per nucleon, releasing energy.
轻核聚变和重核裂变都使产物移向更高平均结合能，从而释放能量。
ΔE = Δm c²
10. Nuclear Fission | 核裂变
Fission is the splitting of a heavy nucleus into two lighter fragments, accompanied by the release of neutrons and a large amount of energy. Uranium‑235 and plutonium‑239 are common fission fuels.
Chain reaction is sustained if at least one neutron per fission triggers another fission; a controlled chain reaction underpins nuclear reactors.
若每次裂变至少有一个中子引发下一次裂变，可实现链式反应；受控链式反应是核反应堆的基础。
11. Nuclear Fusion | 核聚变
Fusion combines light nuclei, such as isotopes of hydrogen, into a heavier nucleus, releasing energy because the product has a greater binding energy per nucleon. Fusion requires extremely high temperatures to overcome Coulomb repulsion.
Absorbed dose (Gy) and equivalent dose (Sv) account for biological effect. Effective dose considers tissue sensitivity.
吸收剂量（Gy）和当量剂量（Sv）考虑生物效应。有效剂量还纳入组织敏感性。
Half‑lives and activity are used to determine safe storage times for nuclear waste.
利用半衰期和活度确定核废料的安全贮存时限。
Master these concepts and practise rearranging decay equations, interpreting binding‑energy graphs, and applying E = mc². You’ll be well prepared for both IB and AQA exams.
掌握以上概念，勤练衰变方程、结合能图线解读及 E = mc² 应用，即可从容应对 IB 和 AQA 考试。
Published by TutorHao | Physics Revision Series | aleveler.com
📚 Mastering Application Techniques for Edexcel IAL Physics Unit 3 (9630-PH03) Mark Scheme v4.2 | 精通爱德思国际 A-Level 物理单元三 (PH03) 应用题技巧：评分标准 v4.2 解读
Unit 3 of the Edexcel International A-Level Physics qualification (9630) is dedicated to practical skills and the application of physics principles to experimental contexts. Many students underestimate the importance of understanding exactly what the mark scheme rewards. This article distils the key application techniques embedded in the PH03 mark scheme v4.2, helping you to craft answers that consistently achieve top marks. We will explore how to structure experimental descriptions, handle uncertainties, draw conclusions, and critically evaluate procedures – all through the lens of the official assessment criteria.
1. Deconstructing the Mark Scheme Mindset | 解读评分标准的思维方式
The PH03 mark scheme is not merely a list of correct answers; it is a map to the examiner’s expectations. Each allocated mark is tied to a specific, demonstrable skill. For an application-based question, the examiner looks for evidence of logical sequencing, appropriate use of apparatus, and quantitative reasoning. Your answer must mirror the concise, bullet-point clarity often seen in the scheme itself. Avoid vague language such as ‘measure it accurately’ – instead specify ‘measure the diameter in three orientations using a micrometer screw gauge and record the mean value to reduce random error’.
Mark for methodology: State what you will do, in the order you will do it.
方法分: 清楚说明你将做什么，并且按执行的顺序叙述。
Mark for justification: Explain why a specific instrument or step is chosen – link it to the precision required or a systematic error to be avoided.
论证分: 解释为何选择特定的仪器或步骤——将其与所需的精确度或需避免的系统误差联系起来。
Mark for analysis: Show how raw data will be transformed into a result, often through a graph or algebraic manipulation.
分析分: 展示如何将原始数据转化为结果，通常通过图像或代数变换。
2. Structuring a Flawless Experimental Procedure | 构建无懈可击的实验步骤
Many PH03 questions begin by asking you to describe an experiment to determine a quantity, such as the resistivity of a wire or the acceleration of free fall. A high-scoring response follows a predictable template. Start with the apparatus list, then move to the manipulation of the independent variable, the measurement of the dependent variable, and finally the control of confounding factors. Never assume the examiner will infer a step; you must write it. For example, if you need to measure the time period of a pendulum, you must state that the timing starts when the bob passes through the equilibrium position, and that ten oscillations are timed to reduce the percentage uncertainty in the period.
Within the scheme, marks are often awarded for a diagram with labelled apparatus. A clear, sketch-like diagram can replace several sentences and demonstrates a solid grasp of the set-up. Ensure your diagram shows how the circuit is completed, where the measuring instruments are placed, and how variables are changed and recorded. If using a travelling microscope or an oscilloscope, label the scale and the quantity being read.
Quantitative application questions invariably require you to combine uncertainties. The mark scheme v4.2 rewards correctly identifying the type of uncertainty and applying the appropriate propagation rule. For addition or subtraction of readings, absolute uncertainties add. For multiplication or division, percentage uncertainties add. When a quantity is raised to a power, such as the radius squared in an area calculation, the percentage uncertainty is multiplied by that power. A common trap is forgetting to multiply the uncertainty in the radius by 2 when calculating the area’s uncertainty. If a micrometer has a resolution of 0.01 mm, the absolute uncertainty in a single reading is ±0.005 mm, but this doubles if you are finding the difference between two readings.
When comparing results, the mark scheme expects a statement about whether the difference between two values is explained by the total experimental uncertainty. You must calculate the percentage difference or absolute difference, compare it to the total percentage or absolute uncertainty, and then conclude whether the results are consistent. A typical phrasing rewarded is: ‘The percentage difference of 4% is less than the total estimated uncertainty of 7%, therefore the results overlap within experimental error and can be considered consistent.’
4. Graph Skills and Interpreting Gradients | 图像技能与斜率解读
Plotting a graph is one of the most heavily weighted application tasks. The mark scheme specifies that axes must be labelled with the quantity and unit, scales must be sensible and use at least half the graph paper, and data points must be plotted accurately to within half a small square. The line of best fit should be drawn to show the trend, ignoring anomalous points that are clearly off the line. If the relationship is expected to be a straight line through the origin, you must state that the line should pass through the origin unless there is a systematic error that justifies an intercept.
To find the gradient, use a large triangle that covers at least half the drawn line, and read the coordinates directly from the best-fit line, not from data points. The gradient calculation must be shown, and its unit must be derived from the ratio of the axes. Many marks are lost because students write the numerical value without a unit. When the gradient is used to determine a physical constant, such as Planck’s constant or the resistivity of a material, you must show the algebraic rearrangement that links the gradient to that constant, and then substitute the gradient value correctly.
5. Critical Evaluation and Identifying Sources of Error | 批判性评价与识别误差来源
A complete application answer typically ends with an evaluation. The mark scheme distinguishes between a generic comment (‘human error’) and a specific, physics-rooted limitation. Effective evaluation identifies a named systematic or random problem, explains its effect on the measured variable, and proposes a realistic and concrete improvement. For example, in an experiment to determine g using a free-fall method, you could state: ‘The electromagnet may release the ball with a delay after the switch is opened, causing the measured time to be smaller than the true time of fall. This leads to an overestimate of g. To reduce this, use a mechanical release mechanism or trigger the timer using a light gate that the ball breaks.’
一个完整的应用答案通常以评价收尾。评分标准区分了泛泛而谈（如“人为误差”）和具体、基于物理的局限性。有效的评价应指出一个提到的系统或随机问题，解释它对被测变量的影响，并提出一个实际且具体的改进。例如，在利用自由落体法测定 g 的实验中，你可以陈述：“电磁铁在开关断开后可能延迟释放小球，导致测得的下降时间比真实时间短。这会使 g 的估计值偏高。为减少此影响，可使用机械释放机构，或用小球切断的光电门来触发计时器。”
Pay attention to percentage uncertainty breakdowns. The mark scheme rewards the candidate who can identify the measurement that contributes the largest percentage uncertainty and then suggest a modification to directly reduce it. If timing a short interval manually yields an uncertainty of ±0.3 s and the time measured is only 1.5 s, the percentage uncertainty is 20%. The improvement must target this specifically: ‘Use a longer drop distance to increase the time interval, reducing the percentage uncertainty of the timing measurement.’
注意百分数不确定度的分解。评分标准奖励能够识别出贡献最大百分数不确定度的测量量，并建议直接减少该不确定度的修改方法的考生。如果手动计时一个短时间间隔产生 ±0.3 s 的不确定度，而测得时间只有 1.5 s，百分数不确定度就是 20%。改进必须专门针对这一点：“使用更长的下落距离以增加时间间隔，减少计时测量的百分数不确定度。”
6. Linking Physics Theory to Practical Steps | 将物理理论与实际步骤联系起来
Application questions in PH03 often ask you to ‘explain how you would use the apparatus’ rather than simply list steps. This requires you to articulate the underlying physics at each stage. If you are using a diffraction grating to determine the wavelength of laser light, you must state that the grating equation d sin θ = nλ is used, and that the angle is measured by noting the positions of the first-order maxima on either side of the central beam and halving the difference to eliminate zero error. The mark scheme rewards this use of symmetry to improve accuracy.
PH03 中的应用题常常要求你“解释你将如何使用仪器”，而不仅仅是罗列步骤。这要求你在每个阶段清晰地阐述背后的物理原理。如果你使用衍射光栅测定激光的波长，你必须说明使用了光栅方程 d sin θ = nλ，并且通过记录中央光束两侧的一级极大位置，将差值减半以消除零点误差，从而测得角度。评分标准奖励这种利用对称性提高精度的做法。
Similarly, when cooling curves are used to determine the specific heat capacity of a liquid, you must explain how the rate of temperature fall at a particular temperature is linked to the power input by electrical heating. The theory is that P = mc (rate of cooling) + heat losses. By performing two experiments – one with electrical heating at a steady temperature and one cooling alone – the cooling rate at that temperature cancels the heat loss term. Describing this compensation method explicitly as per the mark scheme targets the analysis marks.
类似地，当利用冷却曲线测定液体的比热容时，你必须解释在特定温度下的降温速率如何与电加热输入功率联系起来。原理是 P = mc（冷却速率）+ 热损失。通过进行两个实验——一个在恒温下电加热，另一个单独冷却——那个温度下的冷却速率正好与热损失项抵消。按照评分标准明确描述这种补偿方法，直接针对分析分。
7. Handling Incomplete Data and Anomalies | 处理不完整数据与异常值
You may be presented with a table of results and asked to complete missing values or identify anomalous points. The mark scheme v4.2 rewards a systematic approach: first, check the pattern of repeated readings. If a measurement was taken three times and one reading is significantly different, it is likely an anomaly and should be excluded from the mean calculation. When calculating the mean of a set of repeated measurements, you must show the sum and the division, not just the result. The mark scheme often allocates a specific mark for correctly identifying an anomalous value and stating that it must be ignored and possibly repeated if time allows.
When a value is missing from a table, use the physical relationship that defines the experiment to calculate it. For instance, if the table lists applied force and extension, but the spring constant is required, use Hooke’s law F = kx. The mark scheme typically demands that you show the substitution into the equation, not just write the final number. Even if your final answer is incorrect, a correct method may earn partial marks under error-carried-forward principles.
当表格中缺失某个值时，利用定义该实验的物理关系来计算它。例如，如果表格列出了施加的力和伸长量，但要求弹簧劲度系数，就使用胡克定律 F = kx。评分标准通常要求你展示代入方程的过程，而不只是写出最终数字。即使你最后的答案不正确，在错误可延续的原则下，正确的方法仍可获得部分分数。
8. Common Command Words and Their Mark Scheme Implications | 常见指令词及其评分标准含义
Understanding the precise meaning of command words is crucial. ‘Describe’ requires a factual account of what happens or what is done; ‘Explain’ asks for a reason or mechanism, usually linking to a physics principle; ‘Determine’ implies a calculation or a decision based on data; ‘Evaluate’ demands a critical appraisal of the experiment’s strengths and weaknesses. In the context of PH03, an ‘explain’ question often earns marks when you refer to relevant equations or principles explicitly. For instance, ‘Explain why the oscilloscope is set to AC coupling’ should be answered: ‘To block any DC offset and allow only the alternating signal to be displayed, making it easier to measure the peak-to-peak voltage of the waveform.’
Similarly, ‘Suggest’ questions allow you to propose a reasonable adjustment or an interpretation, and the mark scheme will accept any sensible, physics-correct response. However, vague suggestions are not rewarded. If asked to suggest an improvement for reducing the heating effect in a wire, stating ‘use a fan’ will not earn the mark unless you link it to ‘by forced convection to maintain a constant temperature, thereby ensuring resistance does not change’. The link to the measured quantity is the mark earner.
9. Time Management and Answer Presentation | 时间管理与答案呈现
PH03 is a written paper that tests practical thinking, not hands-on dexterity. Efficient time management means avoiding overly long introductions. Start writing your experimental plan immediately, using bullet points if the mark scheme does not forbid them. Keep your sentences short and clear. A mark is often awarded for one specific piece of information; long, rambling paragraphs can bury the key fact and make it harder for the examiner to award it. Use phrases like ‘Measure the potential difference across the wire using a voltmeter’ rather than ‘I would then measure the voltage’. The active, instrumental voice is preferred.
Also, pay attention to the number of marks in square brackets. A [3] mark question typically expects three distinct, non-overlapping points. If you write five sentences but two are essentially rewording the same idea, you will only score for one. Before writing, mentally list the scoring requirements: one mark for the measurement method, one for the data handling, and one for the safety precaution or control of a variable.
10. Examination-Ready Refinements from the Mark Scheme v4.2 | 基于评分标准 v4.2 的考前精练
The latest version 4.2 of the mark scheme places increased emphasis on the justification of measurement techniques. For instance, if you are measuring the thickness of a sheet of paper, stating ‘use a micrometer’ is insufficient; you must clarify that you would measure the thickness of a stack of 50 sheets and divide by 50 to reduce the percentage uncertainty. This technique is praised in multiple places. Similarly, when measuring an oscillating motion, using a light gate and data logger to record the period digitally and eliminate human reaction time is a high-level response that matches the mark scheme’s top descriptors.
Finally, unit conversions and significant figures are constantly checked. The mark scheme often has a specific marking point for expressing the final answer to a consistent number of significant figures, typically the same as the least precise measurement used in the calculation. If your raw data is given to 3 significant figures, your final answer should also be to 3 significant figures. Applying these subtle details consistently will move your script from a middle band to the top band.
📚 Work and Energy: Key Concepts for GCSE CCEA Physics | GCSE CCEA 物理：功与能量 考点精讲
In GCSE CCEA Physics, understanding work and energy is fundamental to explaining how forces cause changes and how energy is conserved. This article breaks down the essential concepts you need to master, from the definition of work done to calculations involving kinetic energy, gravitational potential energy, power, and efficiency. Whether you are preparing for Unit 1 or Unit 2, these clear explanations and worked examples will strengthen your grasp of the topic.
In physics, work is done when a force causes an object to move in the direction of the force. If there is no movement, or if the force is perpendicular to the displacement, no work is done in the scientific sense. For example, holding a heavy book stationary above the ground does not involve work being done on the book, because there is no displacement.
The quantity of work done (W) depends on both the magnitude of the force (F) and the distance (d) moved in the direction of that force. Work is a scalar quantity and is measured in joules (J). One joule is equal to one newton multiplied by one metre.
When the force is applied at an angle, only the component of the force parallel to the displacement contributes to the work done. However, for most GCSE calculations, forces are assumed to act along the line of motion.
To calculate work done, identify the applied force in newtons and the distance moved in metres. Multiply these two values to obtain the work in joules. Always check that the distance used is the one travelled in the direction of the force.
Worked example: A person pushes a trolley with a constant force of 50 N over a distance of 8 m along a flat floor. The work done is:
例题：某人用50 N的恒力沿平地推动一辆手推车，前进了8 m。所做的功为：
W = 50 N × 8 m = 400 J
If the same force is applied but the object does not move (d = 0), then no work is done, no matter how large the force is. This concept often appears in multiple-choice questions.
Energy is defined as the ability to do work. Like work, energy is measured in joules (J). Any system that possesses energy has the potential to exert a force over a distance. Energy exists in many forms, including kinetic, gravitational potential, thermal, chemical, and nuclear.
In GCSE Physics, you will frequently convert between different energy stores and calculate how much work is done when energy is transferred. The link between work and energy is direct: when work is done on an object, energy is transferred to that object; when an object does work, it transfers energy to something else.
Kinetic energy (KE or Ek) is the energy an object possesses due to its motion. Any moving object has kinetic energy. The amount of kinetic energy depends on the object’s mass and its speed.
In this formula, m is the mass in kilograms (kg), and v is the speed in metres per second (m/s). The factor v² means that doubling the speed quadruples the kinetic energy, which has important implications for road safety and impact forces.
Gravitational potential energy (GPE or Ep) is the energy stored in an object due to its position in a gravitational field. The higher the object is lifted, the greater its GPE.
Here, m is mass in kilograms, g is the gravitational field strength (on Earth, approximately 9.8 N/kg, but 10 N/kg is often used in CCEA exams for simplicity), and h is the vertical height in metres above a chosen reference level.
When an object falls, GPE is converted into kinetic energy. The work done by gravity equals the loss in GPE (or gain in KE), assuming no air resistance.
The principle of conservation of energy states that energy cannot be created or destroyed. It can only be transferred from one energy store to another or transformed from one form to another. The total energy of a closed system remains constant.
In an ideal pendulum, the sum of kinetic energy and gravitational potential energy is constant, provided there is no friction or air resistance. As the pendulum swings, energy is continuously exchanged between KE and GPE.
In real systems, some energy is always dissipated as thermal energy due to friction and air resistance. This ‘wasted’ energy spreads into the surroundings and is no longer useful to do work, but it is not destroyed.
Energy transfers can be represented by flow diagrams. Common examples include:
能量传递可以通过流程图来表示。常见的例子包括：
An electric lamp: electrical energy → light energy + thermal energy.
电灯：电能 → 光能 + 热能。
A catapult: elastic potential energy → kinetic energy.
弹弓：弹性势能 → 动能。
A battery-powered motor: chemical energy → electrical energy → kinetic energy + thermal energy.
电池驱动电机：化学能 → 电能 → 动能 + 热能。
Work is the mechanism of energy transfer when a force moves an object. The amount of work done is equal to the energy transferred. For example, when you lift a weight, chemical energy from your muscles does work against gravity, increasing the weight’s GPE.
Power is the rate at which work is done or energy is transferred. It is a measure of how quickly energy is used or produced. Power is measured in watts (W), where 1 watt equals 1 joule per second.
P is power in watts, W is work done in joules, E is energy transferred in joules, and t is time in seconds. A powerful machine does a large amount of work in a short time.
Example: A crane motor lifts a load and does 25,000 J of work in 5 seconds. Its power output is P = 25,000 J / 5 s = 5,000 W (or 5 kW).
例题：一台起重机马达在5秒内提起重物做了25000 J的功。其输出功率为P = 25000 J / 5 s = 5000 W (或5 kW)。
9. Efficiency | 效率
No device is 100% efficient because some energy is always dissipated, usually as thermal energy. The efficiency of a device or process indicates how much of the input energy is converted to useful output energy.
Efficiency = (Useful output energy / Total input energy) × 100%
You can also calculate efficiency using power: Efficiency = (Useful power output / Total power input) × 100%. Efficiency has no units and can be expressed as a decimal or a percentage.
Example: A motor lifts a load, transferring 300 J of useful GPE, but draws 400 J of electrical energy from the supply. Its efficiency = (300 / 400) × 100% = 75%. The remaining 100 J is mainly wasted as heat in the motor and cables.
The work-energy principle connects work done with the change in kinetic energy. The net work done on an object is equal to its change in kinetic energy. This principle is particularly useful for solving problems involving acceleration and braking.
If an object speeds up, work is done on it and its KE increases. If it slows down, it does work (e.g., against brakes or friction) and its KE decreases. This idea helps you understand braking distances: the work done by the braking force equals the initial KE of the vehicle.
11. Sankey Diagrams for Energy Analysis | 能量分析的桑基图
A Sankey diagram is a visual representation of energy transfers. The width of each arrow is proportional to the amount of energy. The input arrow is drawn to scale, and it splits into useful energy output and wasted energy branches.
For example, for a typical light bulb, a Sankey diagram would show a wide arrow for electrical energy input. A narrow arrow branches to represent light energy (useful), and a much wider branch shows thermal energy (wasted). Sankey diagrams quickly communicate the efficiency of a device: the more the useful arrow dominates, the higher the efficiency.
Use correct units: Always convert mass to kg, distance to metres, and time to seconds before substituting into formulas. A common mistake is using grams or centimetres, leading to incorrect joules or watts.
Don’t confuse energy and power: Remember that energy is the total amount of work done or stored, while power is the rate of energy transfer. In graphs and descriptions, check whether the question asks ‘how much energy’ or ‘how much power’.
Energy changes in falling objects: When ignoring air resistance, loss in GPE = gain in KE. Set mgh = ½ mv² to find speed or height. The mass often cancels, so speed depends only on height and g.
下落物体的能量变化：忽略空气阻力时，重力势能的减少量 = 动能的增加量。令 mgh = ½ mv² 来求速度或高度。质量往往可以约掉，因此速度只取决于高度和重力加速度。
Sankey diagram proportions: Ensure the sum of the widths of output arrows equals the width of the input arrow. Label each arrow clearly with the type of energy and the numerical value in joules.
桑基图的比例：确保输出箭头宽度之和等于输入箭头的宽度。清晰地给每个箭头标上能量类型和焦耳数值。
Revision tip: Practise rearranging the kinetic energy and GPE formulas to solve for mass, speed, or height. Worked examples from past CCEA papers are excellent for mastering multi-step energy problems.
📚 Cracking the AS Physics Unit 1 Jan 19 Experimental Investigation | 攻克 AS 物理单元 1 2019 年 1 月实验探究题
The January 2019 Edexcel AS Physics Unit 1 paper presented a compelling practical investigation: using two light gates and a timer to measure the acceleration of a freely falling ball. This type of question tests not only your grasp of kinematic equations but also your ability to handle raw data, evaluate uncertainties, and suggest meaningful improvements. Whether you are revising for your mocks or preparing for the final exam, a thorough walkthrough of this past-paper investigation will sharpen your analytical skills and boost your confidence.
2019 年 1 月 Edexcel AS 物理单元 1 试卷中，展示了一个引人入胜的实验探究：利用两个光门和一个计时器来测量自由下落小球的加速度。这类题目既考查你对运动学方程的掌握，也考验你处理原始数据、评估不确定度和提出有意义的改进措施的能力。无论你是在为模拟考做准备，还是为最终考试冲刺，仔细拆解这道真题探究都将提升你的分析能力并增强应试信心。
1. Overview of the Investigation | 实验探究概述
The goal was to determine the acceleration due to gravity, g, by releasing a metal ball from rest and recording its motion through two light gates placed one above the other. A data logger or timer measured the short time intervals during which the ball interrupted each beam, as well as the time taken to travel from the first gate to the second.
Although a single set of readings was provided in the printed question, the underlying method is identical to a full-scale multiple-measurement experiment. You are expected to use the fundamental definitions of average velocity for a very short time interval, treat it as instantaneous velocity, and then apply the equations of uniformly accelerated motion.
A typical setup includes a rigid stand with two light gates, a steel or brass ball, a millisecond timer connected to the gates, a metre rule, and a micrometer or vernier calipers for measuring the ball’s diameter. The upper gate is placed just below the release point so that the ball is already moving when it enters the first beam, but its initial velocity is not required to be zero – we only need the velocities at each gate and the transit time between them.
The diameter of the ball is critical because the light-gate timing, tgate, is the interval during which the ball’s leading edge enters the beam until its trailing edge leaves. Dividing the diameter by this ‘interruption time’ gives the average velocity. Provided the beam is very narrow and the interruption time is sufficiently short, this average velocity closely approximates the instantaneous velocity at the midpoint of the gate.
In the January 2019 paper, the diameter d was given as 2.00 cm, recorded to three significant figures. Most students would have measured this with a micrometer screw gauge, which can read to ±0.01 mm. If you are repeating such an experiment, take several readings in different orientations to check for spherical symmetry and reduce random error.
在 2019 年 1 月的试卷中，直径 d 给出为 2.00 cm，保留三位有效数字。大多数学生会使用可读至 ±0.01 mm 的千分尺来测量该数据。如果你亲自重复这样的实验，应从不同方向多次测量，以检查球体的对称性并减小随机误差。
Always record the diameter in metres before substituting into velocity equations. Here, d = 0.0200 m. A common slip is to forget converting centimetres to metres, which would throw the velocity values off by a factor of 100.
在代入速度方程前，务必将直径换算为米。此处 d = 0.0200 m。一个常见的疏忽是忘记将厘米转换为米，这会使速度值偏离 100 倍。
4. Instantaneous Velocity at Each Gate | 每个光门处的瞬时速度
The velocity at Gate 1 is found using v1 = d / t1, where t1 is the time the ball takes to pass through the first beam. Similarly, v2 = d / t2 for the second gate. The exam question supplied t1 = 0.0150 s and t2 = 0.0090 s.
光门 1 处的速度用 v1 = d / t1 计算，其中 t1 是小球穿过第一道光束的时间。同理，光门 2 处的速度 v2 = d / t2。试题给出的数据为 t1 = 0.0150 s 和 t2 = 0.0090 s。
Performing the arithmetic:
进行算术运算：
v1 = 0.0200 m ÷ 0.0150 s = 1.333 m s⁻¹ v2 = 0.0200 m ÷ 0.0090 s = 2.222 m s⁻¹
Notice that the ball’s speed increases substantially between the two gates, consistent with acceleration due to gravity.
请注意，小球在两光门之间的速度显著增加，这与重力加速度的作用一致。
5. Time Between the Gates | 光门之间的时间
The timer also recorded the interval t between the instant the ball entered the first gate and the instant it entered the second gate. In the paper, t = 0.400 s. This is not the time the ball spends between the gates; it is the time from the start of the first interruption to the start of the second interruption.
Understanding this distinction is crucial. If the question asked for the time the ball is actually between the gates, you would need to subtract half of t1 and half of t2, but since the acceleration calculation relies on the change in velocity over the interval between the velocity measurement points, using the given t is correct for the equation v2 = v1 + g t.
理解这一区别至关重要。如果题目要求的是小球实际处于两光门之间的时间，你需要减去 t1 和 t2 各自的一半，但因为加速度计算依赖于两个速度测量点之间的速度变化时间，使用所给的 t 对于方程 v2 = v1 + g t 来说是正确的。
6. Deriving the Equation for g | 推导重力加速度 g 的方程
Since the ball moves with constant acceleration (we assume air resistance is negligible), we can use the first SUVAT equation in the direction of motion:
由于小球做匀加速运动（我们假设空气阻力可忽略），我们可以沿运动方向使用第一个 SUVAT 方程：
v = u + g t
Taking the velocity at Gate 1 as the initial velocity u and the velocity at Gate 2 as the final velocity v, we can rearrange to isolate g:
This is the key working equation for the investigation. It does not require the distance between the gates, which simplifies the experimental procedure. The student only needs to measure three time intervals and the ball’s diameter.
7. Data, Substitution and Calculated Value of g | 数据、代入与 g 的计算值
Let us collect the given data in a table for clarity.
让我们将给定数据整理成表格以便清晰查看。
Quantity
Symbol
Value
Unit
Diameter of ball
d
0.0200
m
Time through Gate 1
t1
0.0150
s
Time through Gate 2
t2
0.0090
s
Time between gates
t
0.400
s
Velocity at Gate 1
v1 = d / t1
1.333
m s⁻¹
Velocity at Gate 2
v2 = d / t2
2.222
m s⁻¹
Calc. acceleration
g = (v2 − v1) / t
2.22
m s⁻²
Substituting the values yields g ≈ 2.22 m s⁻², which is far smaller than the accepted 9.81 m s⁻². This discrepancy is deliberate – the exam expects you to recognise that the experiment, as conducted, suffers from significant systematic errors.
代入数值计算得到 g ≈ 2.22 m s⁻²，远小于公认值 9.81 m s⁻²。这一偏差是有意设置的——试题期望你认识到该实验在实施过程中存在显著的系统误差。
8. Plotting a Graph for More Reliable Results | 绘制图表以获得更可靠的结果
While the paper presented a single data set, a better experimental strategy involves repeating the measurement with the second gate at different positions below the first gate. If the distance s between the gates is measured, you can record several pairs of (s, v2² − v1²).
From v2² = v1² + 2 g s, a plot of (v2² − v1²) on the y-axis against s on the x-axis yields a straight line through the origin with slope equal to 2 g. This method reduces the impact of random timing errors and allows you to judge reproducibility from scatter.
由 v2² = v1² + 2 g s 可知，以 (v2² − v1²) 为 y 轴、以 s 为 x 轴作图，会得到一条过原点的直线，其斜率等于 2 g。该方法减弱了随机计时误差的影响，并让你能够根据离散程度判断数据的可重复性。
Even if the graph shows a systematic offset, the slope can still provide an accurate g if the offset is constant. This is a key advantage of graphical analysis over single-point calculations.
即使图中显示出系统偏移，只要偏移恒定，斜率仍可给出准确的 g 值。这是图形分析法相对于单点计算的一个关键优势。
9. Sources of Uncertainty and Error | 不确定度与误差来源
The vast difference between the calculated 2.22 m s⁻² and 9.81 m s⁻² demands a discussion of error sources.
计算值 2.22 m s⁻² 与 9.81 m s⁻² 的巨大差异要求我们对误差来源进行讨论。
1. Air resistance and drag. A small but significant upward force opposes the motion, reducing the resultant acceleration. The effect is pronounced for a small, light ball, especially at higher speeds.
2. Measurement of t1 and t2. The times are very short (of the order of milliseconds). Any uncertainty in the timer, or a slight misalignment of the beam so that it is not perpendicular to the motion, can change the effective interruption path length. The finite beam width also means the average velocity is not exactly the instantaneous velocity at the gate centre.
2. t1 和 t2 的测量。 这两段时间极短
Published by TutorHao | AS Physics Revision Series | aleveler.com
These concise revision notes cover the essential topics for IGCSE OCR Physics, designed to help you quickly recall key definitions, formulas, and concepts before the exam. Each section pairs an English explanation with a Chinese version, so you can reinforce your understanding in both languages.
Speed is the distance travelled per unit time. It is a scalar quantity, meaning it has magnitude only.
速率是单位时间内经过的距离，是标量，只有大小没有方向。
Velocity is speed in a given direction. It is a vector quantity, so both magnitude and direction matter.
速度是给定方向上的速率，是矢量，因此大小和方向都很重要。
Acceleration is the rate of change of velocity: a = (v – u) / t, where u is initial velocity, v is final velocity, and t is the time taken.
加速度是速度的变化率：a = (v – u) / t，其中 u 为初速度，v 为末速度，t 为所用时间。
v = u + at s = ut + ½at² v² = u² + 2as
The gradient of a distance-time graph gives speed. The gradient of a velocity-time graph gives acceleration, and the area under the graph gives displacement.
距离-时间图的斜率表示速率；速度-时间图的斜率表示加速度，图线下的面积表示位移。
2. Forces | 力
A force can change an object’s shape, speed, or direction. Forces are vectors measured in newtons (N).
力可以改变物体的形状、速率或运动方向。力是矢量，单位为牛顿 (N)。
Newton’s second law: F = ma, where F is the resultant force, m is mass, and a is acceleration.
牛顿第二定律：F = ma，其中 F 为合力，m 为质量，a 为加速度。
Mass is the amount of matter in an object (kg), while weight is the force due to gravity (N), given by W = mg on Earth g ≈ 9.8 m/s².
质量是物体所含物质的多少 (kg)，而重力是地球引力产生的力 (N)，由 W = mg 计算，地表 g ≈ 9.8 m/s²。
Inertia is the tendency of an object to resist changes in its motion. Stopping distance = thinking distance + braking distance.
惯性是物体抵抗运动状态变化的趋势。停车距离 = 反应距离 + 制动距离。
Momentum p = mv. In a closed system, total momentum before a collision equals total momentum after (conservation of momentum).
动量 p = mv。在封闭系统中，碰撞前的总动量等于碰撞后的总动量（动量守恒）。
3. Energy | 能量
Energy is measured in joules (J). Forms include kinetic, gravitational potential, elastic, thermal, chemical, nuclear, and more.
能量的单位是焦耳 (J)，形式包括动能、重力势能、弹性势能、热能、化学能、核能等。
KE = ½mv² GPE = mgh
Work done W = Fd, where F is force and d is distance moved in the direction of the force. Power P = W/t or P = E/t (watts, W).
做功 W = Fd，F 为力，d 为沿力方向移动的距离。功率 P = W/t 或 P = E/t，单位为瓦特 (W)。
Efficiency = useful output energy ÷ total input energy × 100%. No device can be more than 100% efficient due to energy dissipated as heat.
Energy cannot be created or destroyed, only transferred, stored, or dissipated. This is the principle of conservation of energy.
能量不能被创造或消灭，只能被转移、储存或耗散。这就是能量守恒定律。
4. Waves | 波
Waves transfer energy without transferring matter. Transverse waves (e.g., light, water ripples) oscillate perpendicular to the direction of energy transfer; longitudinal waves (e.g., sound) oscillate parallel to it.
Here v is wave speed (m/s), f is frequency (Hz), and λ (lambda) is wavelength (m). The period T = 1/f.
式中 v 为波速 (m/s)，f 为频率 (Hz)，λ 为波长 (m)。周期 T = 1/f。
The electromagnetic spectrum, in order of decreasing wavelength: radio, microwave, infrared, visible light, ultraviolet, X-ray, gamma ray. All travel at 3.0×10&sup8; m/s in a vacuum.
Reflection, refraction, and diffraction are wave behaviours. Refraction occurs when waves change speed at a boundary, causing a change in direction unless they strike the boundary along the normal.
In parallel circuits: p.d. is the same across each branch; total current is the sum of branch currents; total resistance is less than the smallest individual resistance.
并联电路中各支路两端电压相等；总电流等于各支路电流之和；总电阻小于最小的单个支路电阻。
Component
Graph characteristic
Fixed resistor
Straight line through origin (ohmic)
Filament lamp
Curve, as resistance increases with temperature
Diode
Forward bias: current flows above threshold; reverse bias: near zero
表：常见元件的 I-V 特性
LDR (light-dependent resistor): resistance decreases as light intensity increases. Thermistor: resistance decreases as temperature increases. Both are used in sensing circuits.
光敏电阻 (LDR)：光照增强时电阻减小。热敏电阻：温度升高时电阻减小。两者都常用于传感电路。
6. Magnetism and Electromagnetism | 磁学与电磁学
A magnet has a north and a south pole. Like poles repel, unlike poles attract. Magnetic field lines go from north to south.
磁体有 N 极和 S 极。同名磁极相互排斥，异名磁极相互吸引。磁感线从 N 极指向 S 极。
An electromagnet is a solenoid with a soft iron core; the magnetic field strength increases with more turns, larger current, or an iron core.
电磁铁是带有软铁芯的螺线管；增加匝数、增大电流或加入铁芯均可增强磁场强度。
The motor effect: a current-carrying wire in a magnetic field experiences a force. Fleming’s left-hand rule gives direction: thumb = force, first finger = field, second finger = current.
A d.c. motor uses a split-ring commutator to reverse current direction every half turn, keeping the coil spinning in one direction.
直流电动机利用换向器每半圈改变电流方向，从而使线圈持续朝同一方向转动。
Electromagnetic induction: a changing magnetic field induces a p.d. across a conductor. For a generator, moving a coil in a magnetic field produces a.c.; slip rings maintain a.c. output.
Transformers change the voltage of an a.c. supply: Vp/Vs = Np/Ns. A step-up transformer has more turns on the secondary coil and increases voltage.
变压器改变交流电压：Vp/Vs = Np/Ns。升压变压器的副线圈匝数更多，用于升高电压。
7. Thermal Physics | 热物理学
Temperature (measured in °C or K) reflects the average kinetic energy of particles. Heat is thermal energy transferred due to a temperature difference.
温度（单位为 °C 或 K）反映了粒子平均动能的大小。热量是因温度差而传递的热能。
Heat transfer methods: conduction (mainly in solids, via particles or free electrons), convection (fluids, via density changes), and radiation (infrared, does not need a medium).
Specific heat capacity c: energy needed to raise 1 kg of a substance by 1 °C. ΔE = m c Δθ. Water has a high specific heat capacity (4200 J/kg°C).
比热容 c：使 1 kg 物质升高 1 °C 所需的能量。ΔE = m c Δθ。水的比热容很高 (4200 J/kg°C)。
Specific latent heat L: energy needed to change the state of 1 kg of a substance without temperature change. E = m L. Latent heat of fusion (melting) and vaporisation (boiling) are key values.
比潜热 L：使 1 kg 物质在不改变温度的情况下发生状态变化所需的能量。E = m L。熔化潜热和汽化潜热是重要的常数。
Gas pressure is caused by particles colliding with container walls. Increasing temperature at constant volume raises pressure because particles move faster and hit walls harder and more often.
An atom consists of a nucleus containing protons and neutrons, surrounded by electrons in energy levels. Proton number Z = atomic number, nucleon number A = mass number.
原子由包含质子和中子的原子核以及分层排布的电子组成。质子数 Z = 原子序数，核子数 A = 质量数。
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons, e.g., ¹⁴₆C and ¹²₆C.
同位素是具有相同质子数但中子数不同的同种元素原子，例如 ¹⁴₆C 和 ¹²₆C。
Radioactive decay: unstable nuclei emit alpha (α, ⁴₂He), beta (β⁻, electron), or gamma (γ, electromagnetic wave) radiation. Alpha is the most ionising but least penetrating; gamma is the most penetrating.
Nuclear fission: a heavy nucleus (e.g., U-235) splits into two smaller nuclei, releasing energy and neutrons, which can trigger a chain reaction.
核裂变：重核（如铀-235）分裂成两个较小的核，释放能量和中子，可能引发链式反应。
Nuclear fusion: two light nuclei (e.g., hydrogen isotopes) join to form a heavier nucleus, releasing vast energy. It occurs in stars.
核聚变：两个轻核（如氢的同位素）结合成一个较重的核，释放巨大能量。聚变发生在恒星内部。
9. Space Physics | 空间物理
Our Solar System contains the Sun, eight planets, dwarf planets, moons, asteroids, and comets. Orbital period depends on distance from the Sun; planets sweep out equal areas in equal times under gravity.
The life cycle of a star depends on its mass. A star like the Sun: nebula → protostar → main sequence → red giant → planetary nebula → white dwarf. More massive stars become red supergiants and may end as supernovae, leaving behind neutron stars or black holes.
Red-shift: light from distant galaxies is shifted toward the red end of the spectrum, indicating they are moving away from us. More distant galaxies show greater red-shift, evidence for an expanding Universe.
The Big Bang theory states the Universe began from a hot, dense point and has been expanding ever since. Cosmic microwave background radiation supports this.
大爆炸理论认为宇宙起源于一个极热、极密的点，并一直在膨胀。宇宙微波背景辐射为该理论提供了支持。
10. Practical Skills | 实验技能
Always record measurements with appropriate units and to an appropriate precision. Use a ruler to measure length, a stopwatch for time, an ammeter in series for current, and a voltmeter in parallel for p.d.
Avoid parallax error by reading the scale with your eye directly perpendicular to the pointer. Repeat readings and calculate a mean to reduce random error.
读数时视线应与刻度垂直，以避免视差。通过重复测量并计算平均值来减小随机误差。
Plot graphs with labelled axes, sensible scales, and plot points as small crosses. Draw a line of best fit; if it passes through the origin, it suggests a direct proportionality.
When describing an investigation, clearly state the independent variable (you change), dependent variable (you measure), and control variables (keep constant).
描述探究实验时，应明确说明自变量（你改变的）、因变量（你测量的）和控制变量（保持不变的）。
Understand the use of standard circuit tests: measuring resistance via V/I, investigating factors affecting resistance, or determining the half-life from a decay curve using a Geiger-Müller tube.
📚 Key Concepts from A-Level Physics Unit 4 January 2021 Mark Scheme | A-Level物理单元4 2021年1月评分方案概念解析
The January 2021 Unit 4 mark scheme for A-Level Physics offers deep insight into the precise understanding and application of concepts examiners expect. This article decodes the key themes — from vector analysis in momentum to field potential and exponential decay — appearing in that session’s assessment. By studying the mark scheme’s emphasis on rigorous definitions, correct use of mathematical models and careful graphical interpretation, students can sharpen their revision and avoid common pitfalls.
The mark scheme repeatedly rewarded candidates who explicitly treated momentum as a vector with positive and negative signs according to a defined direction. In one-dimensional collisions, setting a positive axis and assigning signs to velocities before and after was essential to score full marks.
Calculations using p = mv relied on correct sign conventions, not just magnitude. The scheme penalised answers that simply added magnitudes without considering direction. Momentum conservation was always written as Σp_initial = Σp_final, with each term carrying a ± sign linked to the chosen coordinate system.
使用 p = mv 进行计算需依赖正确的符号约定，而不仅仅是大小。评分方案会对只加大小而不考虑方向的答案扣分。动量守恒始终写作 Σp_初 = Σp_末，每一项都带有与选定坐标系相关联的±号。
Define a clear positive direction before writing equations.
在写方程之前明确设定正方向。
Express total momentum as vector sum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ with signs.
将总动量表示为矢量求和：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂，并带有符号。
The mark scheme also highlighted that impulse I = Δp is a vector; the direction of the force acting matches the change in momentum. Full marks required linking impulse direction to motion change.
评分方案还强调冲量 I = Δp 是矢量；作用力方向与动量变化方向一致。要获得满分需将冲量方向与运动变化联系起来。
2. Centripetal Force and Circular Motion Conditions | 向心力与圆周运动条件
Questions on circular motion demanded clear identification of the resultant force towards the centre. The January 2021 scheme accepted only forces directed to the centre as providing centripetal acceleration; any confusion with tangential forces lost marks.
had to be used with exact radius values. Candidates who substituted diameter for radius were penalised. The scheme also expected explanation that if the centripetal force suddenly vanishes, the object moves tangentially at constant speed due to inertia, not radially outward.
方程 F = mv² / r = mrω² 必须代入精确的半径值。将直径误作半径代入的考生会被扣分。评分方案还期望解释：若向心力突然消失，物体会因惯性沿切线方向匀速运动，而非径向飞出。
Angular speed ω was often requested in rad s⁻¹. The scheme required conversion from revolutions per minute using 1 rev = 2π rad and 1 min = 60 s. Marks were lost for omitting the radian measure or using degrees.
角速度 ω 常要求以 rad s⁻¹ 表示。方案要求由每分钟转数转换为：1 转 = 2π rad，1 min = 60 s。遗漏弧度单位或使用度数会导致失分。
3. Electric Field Strength and Potential Gradients | 电场强度与电势梯度
Examiners carefully split marks between defining electric field strength E = F/q and calculating it from potential gradient E = -ΔV/Δr. The mark scheme insisted on the negative sign when relating field direction to decreasing potential.
考官将电场强度定义 E = F/q 和由电势梯度 E = -ΔV/Δr 计算的分值仔细分开。评分方案在将场方向与电势下降相关联时，坚持要求负号。
In uniform fields,
E = V / d
was accepted only when d was the perpendicular separation between equipotential surfaces. Using slant distance cost marks. The scheme also noted that field lines point from high to low potential, and that positive charges move in the direction of the field.
在匀强电场中，只有当 d 是等势面之间的垂直距离时，E = V / d 才被接受。使用斜线距离会丢失分数。方案还指出电场线由高电势指向低电势，且正电荷沿电场方向运动。
Concept
Common Error
Mark Scheme Requirement
Electric potential V
Mixing with potential energy
V is work done per unit charge (J C⁻¹)
Force on charge
Ignoring sign of q
F = qE; direction depends on sign of q
中文翻译：
概念
常见错误
评分方案要求
电势 V
与电势能混淆
V 是单位电荷做功 (J C⁻¹)
电荷所受的力
忽略 q 的符号
F = qE; 方向取决于 q 的正负
4. Capacitor Energy and Exponential Discharge | 电容器能量与指数放电
The mark scheme stressed that energy stored in a capacitor,
E = ½ CV² = ½ QV = ½ Q²/C
, must be linked to the area under a Q-V graph. Full marks required stating that the triangular area represents energy for a linear Q-V relationship.
评分方案强调电容器储存的能量 E = ½ CV² = ½ QV = ½ Q²/C 必须与 Q-V 图线下的面积联系起来。要获得满分需说明三角形面积代表线性 Q-V 关系对应的能量。
During discharge, the time constant τ = RC determines how fast voltage decays: V = V₀ e⁻ᵗ/ᴿᶜ. The scheme penalised using non-SI units for R and C; τ must be in seconds. Graph interpretation required reading V at t = τ as 0.37V₀, and showing that the graph never reaches zero mathematically.
在放电过程中，时间常数 τ = RC 决定电压衰减的速度：V = V₀ e⁻ᵗ/ᴿᶜ。方案会因 R 和 C 使用非国际单位而扣分；τ 必须以秒为单位。图像解读要求读出 t = τ 时 V 为 0.37V₀，并表明数学上图线永远不会到达零。
The January 2021 scheme also rewarded comments on the constant ratio property: in equal time intervals, the voltage falls by the same factor, not the same amount. This exponential nature was crucial for distinguishing from linear decay.
5. Magnetic Force on Moving Charges and Currents | 运动电荷与电流所受磁力
The equation
F = B Q v sin θ
appeared with emphasis on the angle between velocity and magnetic field. The scheme required stating that maximum force occurs when θ = 90° and zero force when θ = 0° or 180°. The direction was determined by Fleming’s left-hand rule, and the scheme insisted on clear labelling of thumb (force), first finger (field), second finger (conventional current for positive charges).
方程 F = B Q v sin θ 出现时强调速度与磁场之间的夹角。方案要求说明当 θ = 90° 时力最大，θ = 0° 或 180° 时力为零。方向由弗莱明左手定则确定，方案坚持明确标注拇指（力）、食指（场）、中指（正电荷的常规电流方向）。
For a current-carrying conductor,
F = B I L sin θ
, the mark scheme required L to be the length of wire within the magnetic field. Marks were lost if the wire was not perpendicular to the field when maximum force was assumed, unless sin θ was included.
对于载流导体，F = B I L sin θ，评分方案要求 L 是处于磁场中的导线长度。如果假设最大力时导线并不垂直于磁场，且未包含 sin θ，就会失分。
6. Electromagnetic Induction and Faraday’s Law | 电磁感应与法拉第定律
The mark scheme gave credit for stating Faraday’s law in words: induced e.m.f. is proportional to the rate of change of magnetic flux linkage. The equation
ε = -N (ΔΦ / Δt)
had to be applied with correct units for Φ (Wb) and t (s). Lenz’s law (the negative sign) was required to explain the direction of induced e.m.f. opposing the change causing it.
评分方案对用文字表述法拉第定律给予加分：感应电动势与磁通匝链数的变化率成正比。方程 ε = -N (ΔΦ / Δt) 必须使用正确的 Φ (Wb) 和 t (s) 单位。楞次定律（负号）被要求用于解释感应电动势的方向如何反抗引起它的变化。
Questions often involved a coil rotating in a uniform magnetic field, generating alternating e.m.f. Φ = BA cos(ωt). The scheme required differentiation or reasoning that maximum e.m.f. occurs where flux is zero (coil parallel to field) and zero e.m.f. where flux is maximum (coil perpendicular). Understanding this phase relationship was essential.
题目常涉及线圈在匀强磁场中旋转产生交变电动势 Φ = BA cos(ωt)。方案要求通过微分或推理得出：磁通为零时（线圈平行于场）电动势最大，磁通最大时（线圈垂直）电动势为零。理解这种相位关系至关重要。
7. Particle Interactions and Conservation Rules | 粒子相互作用与守恒规则
The mark scheme heavily rewarded systematic application of conservation laws: charge, baryon number, lepton number, and strangeness (in strong interactions). In the January 2021 paper, identifying whether a reaction proceeds via strong or weak interaction often hinged on strangeness conservation.
For beta decay, the scheme required the full equation, e.g., n → p + e⁻ + ν̅ₑ, with antineutrino correctly specified to conserve lepton number. Omitting the antineutrino lost marks, even if charge and baryon numbers were balanced.
对于β衰变，方案要求完整方程，例如 n → p + e⁻ + ν̅ₑ，正确标出反中微子以保持轻子数守恒。遗漏反中微子会失分，即使电荷和重子数已平衡。
Feynman diagrams were marked for correct exchange particles: W⁺ or W⁻ for weak interaction, gluon for strong, photon for electromagnetic. The direction of arrows and time axis had to be consistent with the interaction.
8. Mass–Energy Equivalence and Nuclear Binding Energy | 质能等价与核结合能
Einstein’s
E = m c²
was tested in the context of mass defect and binding energy per nucleon. The mark scheme insisted on converting mass defect from atomic mass units (u) to kilograms or directly using MeV/c² equivalent. The conversion 1 u = 931.5 MeV was frequently needed, and candidates had to express final answers in MeV or J as demanded.
爱因斯坦的 E = m c² 在质量亏损和每个核子的结合能背景下被考查。评分方案坚持将质量亏损从原子质量单位 (u) 换算为千克，或直接使用 MeV/c² 等效值。经常要用到 1 u = 931.5 MeV 的换算，考生必须按要求以 MeV 或 J 表示最终答案。
Binding energy per nucleon graphs were analysed: the scheme expected the curve’s peak around iron-56 to be linked to stability. Fusion releases energy for light nuclei (increasing binding energy per nucleon); fission releases energy for heavy nuclei. Reasoning had to refer to the graph, not general statements.
9. Graph Skills: Gradient and Area in Mechanics | 图像技巧：力学中的斜率与面积
Many Unit 4 questions required extracting physical quantities from graphs. The scheme marked explicitly for using large triangles to find gradients and for counting squares (or integrating) under curves for impulse or work. Incorrect units derived from graph axes lost marks.
A velocity–time graph’s area gives displacement, its gradient acceleration. Force–time area gives impulse. The mark scheme stressed that if the graph is non-linear, simple triangle formulas do not apply; candidates must estimate area by grid methods.
10. Applying SUVAT in Two Dimensions and Projectile Motion | 二维运动与抛体运动中的SUVAT应用
The mark scheme separated horizontal and vertical motion in projectile problems completely. Horizontal velocity was taken as constant (aₓ = 0), vertical motion used a = g = 9.81 m s⁻². Candidates had to show that time of flight was determined purely by vertical motion.
评分方案将抛体问题中的水平和垂直运动完全分开。水平速度视为恒定 (aₓ = 0)，垂直运动使用 a = g = 9.81 m s⁻²。考生必须证明飞行时间完全由垂直运动决定。
Equations like
s = u t + ½ a t²
had to be written with correct signs for the chosen direction. A body projected upward with positive u would have s positive above launch, g acting downward taken as -9.81. The scheme penalised mixing sign conventions within one problem.
方程 s = u t + ½ a t² 必须根据所选方向使用正确的符号。一个以正 u 向上投出的物体，发射点以上 s 为正，向下的 g 取 -9.81。方案会因在同一题目中混用符号规则而扣分。
11. Energy Conservation in Oscillating Systems | 振动系统中的能量守恒
In simple harmonic motion, the exchange between kinetic and potential energy was assessed. The scheme required
E_total = ½ k A² = ½ m ω² A²
for a mass-spring system. Candidates had to explain that at maximum displacement, energy is all potential; at equilibrium, all kinetic. Graphs of kinetic energy vs. displacement are parabolic, and the scheme expected the correct shape with labels.
在简谐运动中，考查了动能与势能之间的转换。方案要求对于弹簧振子系统 E_总 = ½ k A² = ½ m ω² A²。考生需解释在最大位移处，能量全部为势能；在平衡位置，全部为动能。动能-位移图为抛物线，方案期望正确形状并标有注释。
The January 2021 mark scheme accepted damping descriptions only when referring to the gradual loss of total energy due to resistive forces, and the effect on amplitude decay. Saying ‘energy is lost’ without specifying the mechanism was insufficient.
12. Experimental Uncertainties and Data Presentation | 实验不确定度与数据呈现
Data analysis questions rewarded correct calculation of absolute and percentage uncertainties. The scheme insisted that final absolute uncertainties be given to one significant figure (or sometimes two if the first digit is 1) and that the measured value be quoted to the same decimal place.
Log graphs were used to linearise exponential relationships. Taking natural logs of both sides of V = V₀ e⁻ᵗ/ᴿᶜ yields ln V = ln V₀ – t/RC. The mark scheme required labelling axes as ln(V/V) and t/s, not just ln V. Gradient = -1/RC had to be identified with units.
Waves are a core topic in A-Level Physics, bridging mechanical oscillations with light, sound, and the electromagnetic spectrum. A thorough understanding of wave behaviour, from the simplest harmonic descriptions to interference and diffraction, is essential for tackling both theoretical and practical exam questions. This revision guide breaks down the key ideas, formulas, and common pitfalls into twelve focused sections, pairing English explanations with Chinese translations so you can master the content bilingually.
Waves can be classified as transverse or longitudinal. In a transverse wave, particle displacement is perpendicular to the direction of energy propagation (e.g. electromagnetic waves, water ripples, waves on a string). In a longitudinal wave, particle displacement is parallel to the direction of energy propagation (e.g. sound waves, seismic P-waves). Both types transfer energy without net transfer of matter.
波可以分为横波和纵波。在横波中，质点的位移与能量传播方向垂直（例如电磁波、水波、弦上的波）。在纵波中，质点的位移与能量传播方向平行（例如声波、地震 P 波）。两种波都传递能量而不发生物质的净转移。
2. Wave Parameters | 波的基本参数
Key quantities describe any periodic wave. The displacement y of a particle from its equilibrium position is measured in metres. The amplitude A is the maximum displacement. The wavelength λ is the distance between two adjacent points in phase (e.g. crest to crest). The period T is the time for one full oscillation, and the frequency f is the number of cycles per second, measured in hertz (Hz). The relationship f = 1/T always holds. Phase is measured in radians or degrees and determines the state of oscillation at a point.
下列关键量描述任何周期性波。质点偏离平衡位置的位移 y 以米为单位。振幅 A 是最大位移。波长 λ 是两个相邻同相点之间的距离（例如波峰到波峰）。周期 T 是一次完整振动所需的时间，频率 f 是每秒钟的循环次数，单位为赫兹 (Hz)。关系式 f = 1/T 始终成立。相位以弧度或度为单位，决定某一点的振动状态。
3. The Wave Equation | 波动方程
The wave speed v, frequency f and wavelength λ are linked by the wave equation. This equation applies to all waves, provided the medium (or vacuum) is uniform.
波速 v、频率 f 和波长 λ 通过波动方程联系起来。该方程适用于所有波，只要介质（或真空）是均匀的。
v = f λ
Since v is constant for a given medium, increasing the frequency shortens the wavelength. In electromagnetic waves, v = c = 3.00 × 10⁸ m s⁻¹ in a vacuum.
由于在给定介质中 v 是常量，频率增大时波长会变短。对于电磁波，真空中的波速为 v = c = 3.00 × 10⁸ m s⁻¹。
4. Phase and Phase Difference | 相位与相位差
The phase of a wave describes its stage in a cycle, often expressed in radians. Two points on a wave have a phase difference Δφ = (2π/λ) × path difference. When the path difference is a whole number of wavelengths, the points are in phase (Δφ = 0, 2π, 4π …). When the path difference is an odd multiple of half a wavelength, they are in antiphase (Δφ = π, 3π, 5π …). Phase difference is crucial for understanding interference.
When two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements (principle of superposition). For sustained interference, the sources must be coherent – they must have the same frequency and a constant phase difference. Constructive interference occurs when the waves are in phase, giving maximum amplitude. Destructive interference occurs when they are in antiphase, giving minimum amplitude. The path difference condition for constructive interference is nλ (n = 0, 1, 2 …); for destructive interference it is (n + ½)λ.
Young’s experiment demonstrates the wave nature of light. Monochromatic light passes through two narrow slits, acting as coherent sources. An interference pattern of equally spaced bright and dark fringes is observed on a screen. The fringe separation Δx is given by:
where d is the slit separation, D is the distance from slits to screen, and λ is the wavelength. The formula relies on the small-angle approximation. Bright fringes occur where d sinθ = nλ, with n = 0, ±1, ±2 …
其中 d 为双缝间距，D 为缝到屏幕的距离，λ 为波长。该公式基于小角度近似。亮纹出现在满足 d sinθ = nλ 的位置，n = 0, ±1, ±2 …
7. Diffraction and Diffraction Grating | 衍射与衍射光栅
Diffraction is the spreading of waves when they pass through an aperture or around an obstacle. Significant diffraction occurs when the aperture size is comparable to the wavelength. A diffraction grating consists of many equally spaced slits. For a grating with slit spacing d, constructive interference maxima are observed at angles θ given by:
衍射是波通过小孔或绕过障碍物时发生的展宽现象。当小孔尺寸与波长可比时，衍射显著。衍射光栅由许多等间距的狭缝组成。对于缝间距为 d 的光栅，相长干涉的极大出现在满足下式的角度 θ 上：
d sinθ = nλ
where n = 0, ±1, ±2 … (order number). The grating produces sharper, brighter fringes than a double slit and is used to measure wavelengths precisely. The maximum order n is limited by sinθ ≤ 1.
其中 n = 0, ±1, ±2 …（级次）。光栅产生的条纹比双缝更锐利、更亮，且常用于精确测量波长。最大级次 n 受 sinθ ≤ 1 的限制。
8. Stationary Waves | 驻波
A stationary (standing) wave forms when two identical progressive waves travel in opposite directions and superpose. Unlike progressive waves, stationary waves do not transfer energy; they store it in a pattern of nodes (zero displacement) and antinodes (maximum displacement). For a string fixed at both ends, the resonant frequencies are:
Here L is the length of the string and v is the wave speed. The fundamental frequency f₁ occurs when n = 1. The distance between adjacent nodes (or antinodes) is λ/2. In pipes (open or closed), similar standing waves form with different harmonic series.
其中 L 是弦长，v 是波速。基频 f₁ 在 n = 1 时出现。相邻节点（或相邻腹点）之间的距离为 λ/2。在管乐器（开管或闭管）中，也会形成类似的驻波，但谐波序列有所不同。
9. The Doppler Effect | 多普勒效应
The Doppler effect is the change in observed frequency when a wave source and observer move relative to each other. For sound, the observed frequency fₒ is related to the source frequency fₛ by:
where v is the wave speed, vₒ is the observer’s speed, and vₛ is the source speed. Choose the top signs (+) for relative approach (higher frequency) and the bottom signs (−) for relative recession (lower frequency). For light, the Doppler shift produces redshift (receding) and blueshift (approaching) and is used in astrophysics.
其中 v 是波速，vₒ 是观察者速度，vₛ 是波源速度。分子取加号、分母取减号表示相互靠近（频率变高）；分子取减号、分母取加号表示相互远离（频率变低）。对于光，多普勒频移产生红移（远离）和蓝移（靠近），在天体物理学中得到应用。
10. Polarisation | 偏振
Polarisation is a property unique to transverse waves. An unpolarised wave vibrates in all planes perpendicular to the direction of propagation. After passing through a polarising filter (e.g. a polaroid film), the wave oscillates in only one plane. For light, Malus’s law describes the transmitted intensity through a second polariser (analyser) at angle θ:
where I₀ is the intensity after the first polariser. Polarisation provides evidence that light is a transverse wave. Applications include glare-reducing sunglasses, LCD screens, and stress analysis in materials.
Electromagnetic (EM) waves are transverse waves consisting of oscillating electric and magnetic fields. All EM waves travel at the speed of light c in vacuum and differ only in frequency and wavelength. The spectrum, in order of increasing frequency (decreasing wavelength), is: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Each region has distinct properties and uses.
电磁波是由振荡的电场和磁场组成的横波。所有电磁波在真空中都以光速 c 传播，仅在频率和波长上存在差异。电磁波谱按频率递增（波长递减）的顺序依次为：无线电波、微波、红外线、可见光、紫外线、X 射线和伽马射线。每一区域都具有不同的特性和用途。
Region / 区域
Wavelength range / 波长范围
Typical application / 典型应用
Radio / 无线电波
> 0.1 m
Communication, MRI
Microwave / 微波
1 mm – 0.1 m
Cooking, radar, Wi-Fi
Infrared / 红外线
700 nm – 1 mm
Thermal imaging, remote controls
Visible / 可见光
400 – 700 nm
Human vision, photography
Ultraviolet / 紫外线
10 – 400 nm
Sterilisation, fluorescent lamps
X-rays / X 射线
0.01 – 10 nm
Medical imaging, security
Gamma rays / 伽马射线
< 0.01 nm
Cancer therapy, sterilisation
The energy of an EM photon is E = hf, where h is Planck’s constant. Higher frequency radiation carries more energy per photon.
电磁波光子的能量为 E = hf，其中 h 为普朗克常量。频率越高的辐射，每个光子携带的能量越大。
12. Refraction and Total Internal Reflection | 折射与全内反射
When a wave passes from one medium to another, its speed changes, causing a change in direction – refraction. Frequency remains constant, but wavelength and speed alter. Snell’s law relates the angles of incidence θ₁ and refraction θ₂ to the refractive indices n₁ and n₂:
The refractive index n of a medium is the ratio of the speed of light in vacuum c to its speed in the medium v: n = c / v. When light travels from a denser to a rarer medium (n₁ > n₂), total internal reflection can occur if the angle of incidence exceeds the critical angle θc, given by:
介质的折射率 n 定义为光在真空中的速度 c 与在该介质中的速度 v 之比：n = c / v。当光从光密介质射向光疏介质 (n₁ > n₂) 时，若入射角超过临界角 θc，就会发生全内反射，临界角满足：
sinθc = n₂ / n₁
This principle is exploited in optical fibres, where light is trapped inside the core, enabling high-speed data transmission.
这一原理被应用于光纤中，光被限制在纤芯内传输，从而实现高速数据通信。
Published by TutorHao | Physics Revision Series | aleveler.com
📚 IB vs CCEA Physics: Knowledge Points Comparison | IB与CCEA物理知识点对比
Choosing between the International Baccalaureate (IB) Diploma and the CCEA A-level can be challenging for students aiming to study physics at university. Both programmes cover a broad range of topics, but they differ significantly in structure, depth, and assessment style. This article compares the key knowledge points of IB Physics and CCEA Physics, highlighting differences in mechanics, waves, electricity, quantum physics, practical work, and mathematical demand. Understanding these contrasts will help students, parents, and teachers make informed decisions about which pathway suits particular learning goals.
1. Overview of IB and CCEA Physics Curricula | IB与CCEA物理课程概览
The IB Physics course is offered at Standard Level (SL) and Higher Level (HL). SL covers eight core topics plus one optional topic, while HL covers the same core but with added depth and six additional HL topics, plus one optional topic. Internal assessment (IA), comprising a student-designed investigation, accounts for 20% of the final grade. CCEA A-level Physics is linear, with AS units covering foundation topics and A2 units delving into advanced concepts. It includes three externally assessed written papers and a practical skills unit (or teacher-assessed practical endorsement), with no single large project like the IA.
In terms of content breadth, IB Physics aims for a global perspective, including topics like energy production and relativity (as an option). CCEA Physics places more emphasis on applying mathematical models to real-world engineering problems, with specific units on deformation of solids and astronomy. Both curricula require knowledge of SI units, uncertainty, and data analysis, but IB integrates these skills more explicitly into the core under “Measurements and Uncertainties”.
Both IB and CCEA cover kinematics, Newton’s laws, work, energy, and power. However, IB Physics places a strong conceptual focus on motion graphs and vector resolution, often using ticker-tape or data-logging analysis in practicals. CCEA introduces the equations of motion early and expects students to handle multi-step calculations with constant acceleration, including projectile motion right from AS Unit 1.
IB 和 CCEA 都涵盖运动学、牛顿定律、功、能和功率。然而，IB 物理非常强调运动图像和矢量分解的概念，实验中常采用打点计时器或数据记录分析。CCEA 早期就引入运动方程，并要求学生处理匀加速的多步计算，包括 AS 第一单元中的抛体运动。
Momentum impulse and conservation of momentum appear in both syllabi. IB includes elastic and inelastic collisions, with HL students solving two-dimensional collision problems using vectors. CCEA A2 develops momentum further alongside circular motion and oscillatory systems, incorporating calculus-based derivation for variable forces in certain contexts. One noticeable difference is the treatment of circular motion: IB HL requires understanding centripetal acceleration a = v²/r derivation, while CCEA introduces it at A2 and connects it with gravitational fields and satellite motion.
Wave properties such as reflection, refraction, diffraction, superposition, and standing waves are covered by both boards. IB dedicates a whole core topic to waves (Topic 4) and an HL additional topic (Topic 9: Wave Phenomena), where single-slit diffraction, resolution, and the Doppler effect are studied in depth. CCEA handles waves in AS Unit 2, covering diffraction gratings, progressive and stationary waves, and interference, but leaves the quantitative treatment of single-slit diffraction and the Rayleigh criterion outside the main specification.
反射、折射、衍射、叠加和驻波等波的特性在两个考试局均有覆盖。IB 将波动作为整个核心主题（主题 4），并设有一个 HL 附加主题（主题 9：波动现象），深入学习单缝衍射、分辨率和多普勒效应。CCEA 在 AS 第二单元处理波动，涵盖衍射光栅、行波与驻波以及干涉，但未将单缝衍射的定量处理和瑞利判据纳入主要大纲。
Optics: IB explores lenses and mirrors through ray diagrams and the thin lens equation. CCEA also covers lenses but with a stronger emphasis on derivation of magnification and lens power. The electromagnetic spectrum is present in both specifications; IB includes it under “Wave behavior” while CCEA categorizes it under “Photons” and wave-particle duality. A key contrast is that IB HL requires knowledge of polarization and Malus’s law, which is not explicitly required by CCEA.
Both courses introduce electric fields, current, resistance, circuit analysis, and internal resistance. IB includes Kirchhoff’s laws and potential dividers, and HL extends to capacitance and electromagnetic induction. CCEA AS Unit 1 covers DC circuits thoroughly, with practical work on resistivity and EMF. At A2, CCEA examines capacitors in DC circuits, time constant τ = RC, and magnetic fields, along with Faraday’s and Lenz’s laws. This aligns well with IB HL content, but CCEA tends to include more contextualised engineering examples such as the function of transformers in the National Grid.
The concept of magnetic flux and flux linkage appears in both specifications, but IB HL uses the formula ε = -N (ΔΦ/Δt) and expects students to handle situations with rotating coils. CCEA also requires this, particularly in generator applications. A notable difference is that IB offers an optional topic on electromagnetic induction (Option B) where AC generators and power transmission are explored, while CCEA embeds this material in the core A2 units, making it mandatory for all candidates.
IB Physics covers thermal concepts in Topic 3: thermal energy transfers, specific heat capacity, latent heat, and ideal gases. The kinetic model and molecular interpretation of temperature are explored. HL students derive the pressure formula p = ⅓ ρ and work with the ideal gas law in terms of the Boltzmann constant. CCEA addresses thermal physics in A2 Unit 1, including specific heat capacity, change of state, and the gas laws. However, the kinetic theory derivation using molecular speed distribution is less prominent; instead, CCEA emphasises the practical determination of specific heat capacities and the experimental verification of Boyle’s and Charles’ laws.
Entropy and the second law of thermodynamics are not required by CCEA, whereas IB HL introduces the concept of entropy and irreversible processes qualitatively under the “Thermodynamics” topic. This reflects IB’s tendency toward broader conceptual awareness, while CCEA focuses on practical and calculational aspects of thermal physics.
Quantum physics forms a core part of both specifications. IB SL and HL cover the photoelectric effect, Einstein’s photon model, and atomic energy levels. HL extends this to the de Broglie wavelength, wave-particle duality, and the Bohr model with quantized angular momentum. CCEA places quantum phenomena in AS Unit 2: photons, the photoelectric equation hf = Φ + Ek max, line spectra, and electron energy levels in atoms. In A2, particle physics and wave-particle duality are treated together, with the de Broglie relation and electron diffraction.
量子物理是两个大纲的核心部分。IB 的 SL 和 HL 均涵盖光电效应、爱因斯坦光子模型和原子能级。HL 进一步延伸至德布罗意波长、波粒二象性以及具有量子化角动量的玻尔模型。CCEA 将量子现象置于 AS 第二单元：光子、光电方程 hf = Φ + Ek max、线状光谱和原子中的电子能级。在 A2，粒子物理与波粒二象性共同处理，包括德布罗意关系和电子衍射。
A major difference is the treatment of the uncertainty principle. IB HL includes Heisenberg’s uncertainty principle for position-momentum and energy-time, requiring qualitative understanding and simple estimates. CCEA does not mandate this. Additionally, IB offers an option on “Quantum and Nuclear Physics” that includes the Schrödinger model and tunnelling, far beyond CCEA’s scope.
IB covers radioactive decay, half-life, nuclear reactions, and binding energy in the core, with HL adding fundamental particles, quarks, leptons, and exchange particles. CCEA A2 Unit 2 includes radioactivity and nuclear energy, plus a substantial section on particle physics: leptons, hadrons, baryons, mesons, and the standard model. Both specifications require the interpretation of Feynman diagrams, but CCEA delves deeper into particle interactions and conservation laws, often using more complex diagrams compared to IB’s simpler approach.
Nuclear fission and fusion, critical for energy production, are discussed in both. IB’s optional topic “Energy Production” can extend into detailed nuclear reactor designs, whereas CCEA handles fission and fusion in the core relatively concisely, focusing on equations and energy release calculations.
8. Practical Work and Internal Assessment | 实验操作与内部评估
One of the starkest contrasts lies in practical assessment. IB Physics mandates a compulsory internal assessment: a single 10-hour scientific investigation that is teacher-assessed and externally moderated. Students design their own experiment, collect data, and produce a written report. This accounts for 20% of the final grade and demands independent research skills and personal engagement. CCEA’s practical component is assessed through a separate unit (AS 3 and A2 3) involving practical skills tasks and written exams based on prescribed techniques, or, in some versions, a teacher-assessed practical endorsement that does not contribute to the overall grade but is recorded separately.
The skill sets nurtured differ: IB emphasises inquiry, error propagation, and evaluation of experimental design, while CCEA focuses on proficiency in standard apparatus, accuracy, and data recording. Students who excel in self-directed long-term projects may find the IB IA rewarding, whereas those who prefer systematic skill checklists might lean towards CCEA.
所培养的技能组合不同：IB 强调探究、误差传播和实验设计评价，而 CCEA 侧重标准仪器操作的熟练度、准确度和数据记录。擅长自主长期项目的学生可能会发现 IB IA 更具成就感，而偏好系统化技能清单的学生可能倾向 CCEA。
9. Mathematical Demands | 数学要求
Both qualifications require a strong grasp of algebra and trigonometry. IB Physics expects students to handle rearrangements, exponentials, logs, and simple differential equations indirectly (through derived formulas). Error analysis requires students to compute uncertainties through propagation rules. CCEA also uses calculus in A2, especially for showing how a = -ω²x leads to simple harmonic motion equations and for capacitor discharge. However, CCEA often steps through the derivations more formally, sometimes requiring students to derive expressions from first principles using integration.
两种资格都要求牢固掌握代数和三角学。IB 物理期望学生处理公式变换、指数、对数，并通过导出公式间接运用简单微分方程。误差分析要求学生使用传播规则计算不确定度。CCEA 在 A2 同样使用微积分，尤其是展示 a = -ω²x 如何导出简谐运动方程以及电容放电。不过，CCEA 常更正式地给出推导步骤，有时要求学生通过积分从基本原理推导表达式。
Graphical skills: IB lab reports require computer-aided graphing with maximum-minimum slope to determine uncertainty, while CCEA exam papers frequently ask students to plot graphs, calculate gradients, and interpret intercepts manually. Both involve significant use of trigonometric functions in wave and mechanics contexts.
IB Physics and CCEA Physics both provide rigorous preparation for university studies in science and engineering, yet they cater to different learner profiles. IB offers a holistic, concept-driven programme with a global outlook, integrating theory of knowledge and extended essay elements that foster critical thinking. Its internal assessment develops experience in authentic scientific investigation. CCEA offers a structured, mathematically intensive route with a strong link to applied physics and clear progression through defined units, making it appealing for students who excel in systematic learning and quantitative problem-solving.
When deciding, consider your academic strengths: if you enjoy independent research, broad conceptual connections, and cross-curricular learning, IB Physics may be more rewarding. If you prefer a linear syllabus, detailed mathematical derivations, and practical skill building tested in written papers, CCEA could be the better fit. Ultimately, both will equip you with the fundamental knowledge of physics required for higher education.
📚 Astrophysics for IGCSE AQA Physics | IGCSE AQA 物理天体物理考点精讲
This revision guide covers the essential topics in astrophysics for the AQA IGCSE Physics specification. From the structure of our Solar System to the life cycles of stars, orbital motion, redshift, the Big Bang theory, and artificial satellites, you will find clear explanations and key facts to support your exam preparation.
1. The Solar System: Our Cosmic Neighbourhood | 太阳系：我们的宇宙邻居
The Solar System consists of the Sun, eight planets, dwarf planets (such as Pluto), the asteroid belt, comets, and numerous moons. The four inner planets — Mercury, Venus, Earth, and Mars — are rocky and relatively small, while the four outer planets — Jupiter, Saturn, Uranus, and Neptune — are gas giants, much larger and composed mainly of hydrogen and helium.
The asteroid belt lies between Mars and Jupiter, containing countless rocky bodies. Comets originate from the Kuiper Belt or the Oort Cloud and have highly elliptical orbits, developing glowing tails when they approach the Sun.
Distances within the Solar System are often measured in astronomical units (AU), where 1 AU is the average Earth–Sun distance (about 150 million km). For interstellar distances, the light-year (ly) is used — the distance light travels in one year.
太阳系内的距离常用天文单位（AU）表示，1 AU 是地球与太阳之间的平均距离（约1.5亿千米）。对于星际间的距离，则使用光年（ly）——光在一年内行进的距离。
2. Orbits and Gravity: The Invisible Tether | 轨道与引力：无形的牵引
Planets orbit the Sun, and moons orbit planets, because of the gravitational attraction between masses. For a stable circular orbit, the force of gravity provides the necessary centripetal force directed towards the centre of the orbit.
The orbital speed of a planet depends on its distance from the Sun: the closer the planet, the greater its orbital speed. Similarly, satellites in lower orbits around Earth move faster than those in higher orbits. The orbital period (time for one complete orbit) increases with orbital radius.
If a satellite’s speed were suddenly reduced, it would spiral inwards due to insufficient centripetal force. If it gained too much speed, it would move outwards to a higher orbit or escape if it reached escape velocity.
Gravity on a planet’s surface depends on the planet’s mass and radius. The gravitational field strength g on Earth is approximately 9.8 N/kg, while on the Moon it is about 1.6 N/kg.
行星表面的重力取决于行星的质量和半径。地球表面的引力场强度 g 约为 9.8 N/kg，而月球表面大约为 1.6 N/kg。
3. Life Cycle of Stars – From Nebula to Main Sequence | 恒星的生命周期——从星云到主序星
Stars are born in giant clouds of dust and gas called nebulae. Gravity pulls the material together, forming a dense core — a protostar. As the protostar contracts, its core temperature rises dramatically.
When the core temperature reaches about 15 million kelvin, nuclear fusion of hydrogen into helium begins, releasing enormous amounts of energy. The outward pressure from fusion balances the inward pull of gravity, marking the star’s entry into the main sequence phase. During this stable period, the star is in hydrostatic equilibrium.
A star remains on the main sequence for most of its life. The Sun is a main sequence star and will stay in this phase for about 10 billion years in total.
恒星一生中大部分时间都停留在主序星阶段。太阳是一颗主序星，它将在这个阶段停留约 100 亿年。
4. The Death of Low-Mass Stars (like the Sun) | 低质量恒星（类似太阳）的死亡
When the hydrogen fuel in the core is exhausted, the core contracts under gravity and heats up, while the outer layers expand and cool. The star becomes a red giant. Helium fusion into carbon and oxygen begins in the core.
Eventually, the outer layers are gently ejected, forming a colourful planetary nebula. The hot, dense core left behind is called a white dwarf — a very dense, Earth-sized object that no longer undergoes fusion.
Over billions of years, the white dwarf cools and fades, theoretically becoming a black dwarf. Fusion in low-mass stars only produces elements up to carbon and oxygen.
Stars much more massive than the Sun run out of hydrogen more quickly and swell into red supergiants. The immense core temperature and pressure allow fusion of heavier elements — carbon, neon, oxygen, silicon — until an iron core is produced.
Iron fusion absorbs energy rather than releasing it, so the core suddenly collapses under gravity, triggering a catastrophic supernova explosion. The shock wave ejects the outer layers into space, spreading heavy elements across the cosmos.
The collapsed core becomes either a neutron star — an incredibly dense object made almost entirely of neutrons — or, if the original star was extremely massive, a black hole, where gravity is so strong that not even light can escape.
Elements heavier than iron, such as gold and uranium, are created during the supernova explosion and through rapid neutron capture processes, enriching the universe with the building blocks of planets and life.
When astronomers observe light from distant galaxies, the dark absorption lines in their spectra are shifted towards the red end of the spectrum compared to a laboratory source. This phenomenon is called redshift.
Redshift occurs because the galaxies are moving away from us, stretching the wavelength of light. The amount of redshift z is given by:
红移的产生是因为星系正在远离我们，从而拉长了光的波长。红移量 z 由下式给出：
z = Δλ / λ ≈ v / c
where Δλ is the change in wavelength, λ is the original wavelength, v is the recession speed of the galaxy, and c is the speed of light. For most distant galaxies, v is much less than c, so the approximation holds.
Edwin Hubble discovered that more distant galaxies have larger redshifts, meaning they are receding faster. This relationship, known as Hubble’s Law, is:
埃德温·哈勃发现，越遥远的星系红移越大，意味着它们正在更快地远离。这一关系被称为哈勃定律，表示为：
v = H₀ × d
where H₀ is the Hubble constant (approximately 2.2 × 10⁻¹⁸ s⁻¹ or 70 km/s/Mpc). The law implies the whole universe is expanding uniformly.
7. The Big Bang Theory and Observational Evidence | 大爆炸理论与观测证据
The Big Bang theory states that the universe began about 13.8 billion years ago from an infinitely hot, dense point. Space itself expanded and cooled, allowing the formation of matter, galaxies, and stars.
Two major pieces of evidence support the Big Bang model. First, the redshift of distant galaxies shows that the universe is expanding, which implies a beginning from a single point if we trace the motion backwards in time.
Second, the cosmic microwave background radiation (CMBR) was discovered as a faint microwave glow coming from all directions in space. It corresponds to a temperature of about 2.7 K and is the cooled remnant of the radiation that filled the early universe roughly 380 000 years after the Big Bang.
The uniformity of the CMBR and its spectrum perfectly match theoretical predictions, making it a cornerstone of modern cosmology.
CMBR 的均匀性及其光谱与理论预测完美吻合，使其成为现代宇宙学的基石。
8. Artificial Satellites and Their Orbits | 人造卫星及其轨道
Artificial satellites are objects placed into orbit around Earth for purposes such as communication, weather observation, navigation, and scientific research. They rely on gravity to provide the centripetal force for circular motion.
Geostationary satellites orbit at an altitude of approximately 36 000 km above the equator. Their orbital period is exactly 24 hours, so they appear stationary relative to a fixed point on Earth’s surface. These are ideal for telecommunications and TV broadcasting.
地球静止轨道卫星在赤道上空约 36 000 km 的高度运行。其轨道周期正好为 24 小时，因此相对于地面上的固定点看起来静止不动。这类卫星非常适合通信和电视广播。
Polar orbit satellites travel at much lower altitudes (typically 200–1000 km) and pass over or near the Earth’s poles. As the Earth rotates beneath them, they can scan the entire surface over time, making them useful for Earth observation, weather monitoring, and military surveillance.
For a satellite in a stable circular orbit, the orbital speed depends on its distance from Earth’s centre: the smaller the orbital radius, the greater the speed required. This relationship ensures the centripetal force matches the gravitational pull exactly.
Medical physics applies the principles of waves, radiation and electromagnetism to diagnose and treat disease. This topic is a favourite on OCR IGCSE papers, as it brings together many core physics concepts in a real‑world context. In this article we will walk through every essential idea – from X‑ray production to ultrasound imaging – pairing clear English explanations with precise Chinese translations so that you can master the content in both languages.
医疗物理将波动、辐射和电磁学原理应用于疾病的诊断与治疗。这个主题是 OCR IGCSE 试卷的常客，因为它把许多核心物理概念融入了现实情境。本文我们将逐一梳理每个关键知识点——从 X 射线的产生到超声波成像——并用清晰的英文解释与准确的中文翻译配对，帮助你用两种语言掌握内容。
1. Introduction to Medical Physics | 医疗物理导论
Medical physics uses ionising and non‑ionising radiation to see inside the body and to destroy harmful cells. The main techniques are X‑ray imaging, CT scanning, ultrasound, endoscopy and nuclear medicine. Each method relies on a different part of the electromagnetic spectrum or on mechanical waves, and each has a different balance of risk and benefit.
医疗物理利用电离辐射和非电离辐射来观察人体内部和摧毁有害细胞。主要技术有 X 射线成像、CT 扫描、超声波、内窥镜检查和核医学。每种方法依赖电磁波谱的不同部分或机械波，各自有不同的风险与益处权衡。
In OCR IGCSE you are expected to explain how images are formed, compare techniques in terms of resolution, safety and cost, and describe how physics limits what we can see.
X‑rays are high‑frequency, high‑energy electromagnetic waves with wavelengths around 10⁻¹⁰ m. They are produced when fast‑moving electrons are suddenly decelerated by a metal target – this is called braking radiation or Bremsstrahlung. In an X‑ray tube, a heated filament (cathode) emits electrons by thermionic emission. A high potential difference (p.d.) accelerates these electrons towards a tungsten anode. When the electrons strike the anode, about 1% of their kinetic energy is converted into X‑rays; the rest becomes heat, so the anode must be rotated and cooled.
X 射线是高频高能的电磁波，波长约 10⁻¹⁰ m。当高速电子被金属靶突然减速时就会产生 X 射线——这叫做制动辐射或轫致辐射。在 X 射线管中，加热的灯丝（阴极）通过热电子发射释放电子。高电势差将这电子加速飞向钨靶阳极。当电子撞击阳极时，其动能约 1% 转化为 X 射线；其余变成热量，因此阳极必须旋转并冷却。
The intensity (rate of energy arriving) of the X‑ray beam can be increased by raising the tube current (more electrons per second), while the hardness (penetrating power) can be increased by raising the accelerating p.d. (giving each electron more energy).
X 射线束的强度（能量到达速率）可以通过增大管电流（每秒更多电子）来提高，而硬度（穿透能力）可以通过提高加速电压（给每个电子更多能量）来增强。
Properties: travel in straight lines, affect photographic film, cause fluorescence, ionise gases, penetrate matter more easily the higher the photon energy.
性质：直线传播、使照相底片感光、引起荧光、使气体电离、光子能量越高越容易穿透物质。
3. X‑ray Imaging and Safety | X 射线成像与安全
A conventional X‑ray image is a shadow picture. The patient is placed between the X‑ray source and a detector (photographic film or digital sensor). Dense materials like bone absorb X‑rays strongly because they contain elements with high atomic number (e.g. calcium), so fewer X‑rays reach the detector, leaving a white shadow on a negative. Soft tissue allows more X‑rays to pass through, producing darker regions.
传统的 X 射线图像是一张阴影照片。病人位于 X 射线源和探测器（照相底片或数字传感器）之间。像骨骼这样的致密物质会强烈吸收 X 射线，因为它们含有高原子序数的元素（如钙），因此到达探测器的 X 射线较少，在底片上留下白色阴影。软组织允许更多 X 射线透过，产生较暗区域。
To improve contrast for soft‑tissue organs, a contrast medium such as barium (for a barium meal) or iodine can be swallowed or injected. These materials have high atomic number and so absorb X‑rays strongly, outlining the organ.
为了改善软组织器官的对比度，可吞服或注射造影剂，如钡（做钡餐）或碘。这些材料原子序数高，能强烈吸收 X 射线，勾勒出器官轮廓。
Hazards: X‑rays are ionising radiation. They can damage DNA and cause mutations or cancer. Precautions include shielding (lead aprons), minimising exposure time, using the smallest possible dose (ALARA principle), and never X‑raying pregnant women unless absolutely necessary. Radiographers stand behind lead screens or leave the room during exposure.
危害：X 射线是电离辐射。它们会损伤 DNA，引发突变或癌症。防护措施包括屏蔽（铅围裙）、缩短暴露时间、采用尽可能小的剂量（ALARA 原则），以及除非绝对必要不对孕妇进行 X 光检查。放射技师在曝光时站在铅屏风后面或离开房间。
4. CT Scans | CT 扫描
A Computed Tomography (CT) scanner produces a 3D image by taking many X‑ray ‘slices’ from different angles. The patient lies on a motorised table that moves through a rotating gantry containing an X‑ray tube and an array of detectors. For each thin slice, the tube and detectors rotate, recording the absorption of X‑rays along thousands of paths. A computer then reconstructs a cross‑sectional image (tomogram). By stacking many slices, a 3D digital model is built.
计算机断层扫描 (CT) 通过从不同角度拍摄许多 X 射线“切片”来生成三维图像。病人躺在电动床上，穿过一个旋转机架，机架内装有 X 射线管和一组探测器。对于每个薄层，射线管和探测器旋转，记录 X 射线沿数千条路径的吸收情况。然后计算机重建出横断面图像（断层图）。通过堆叠许多切片，就建立了一个三维数字模型。
Advantages: CT images have very high spatial resolution (can distinguish small structures) and distinguish overlapping organs much better than a plain X‑ray. Disadvantages: a CT scan delivers a radiation dose around 100 times higher than a chest X‑ray, and the machines are very expensive.
优点：CT 图像空间分辨率很高（可分辨细小结构），与普通 X 光相比，能更好地区分重叠的器官。缺点：CT 扫描的辐射剂量大约是胸部 X 光片的 100 倍，且设备非常昂贵。
5. Ultrasound: Principles and Properties | 超声波的原理与性质
Ultrasound refers to sound waves with frequencies above the human hearing range (typically 2–18 MHz for medical use). Unlike X‑rays, ultrasound is non‑ionising and therefore safer for soft tissue and for monitoring unborn babies. It is a longitudinal mechanical wave that requires a medium; it cannot travel through a vacuum.
超声波指频率超过人耳听力范围（医学常用 2–18 MHz）的声波。与 X 射线不同，超声波是非电离的，因此对软组织和胎儿监测更安全。它是一种需要介质的纵机械波，不能在真空中传播。
When ultrasound waves reach a boundary between two tissues with different acoustic impedances, part of the wave is reflected and part is transmitted. The acoustic impedance Z of a material is given by Z = ρc, where ρ is the density and c is the speed of sound in the material. The greater the difference in Z, the larger the reflected fraction. This is the basis for ultrasound imaging.
当超声波到达两种具有不同声阻抗的组织之间的边界时，一部分波被反射，一部分被透射。材料的声阻抗 Z 由 Z = ρc 给出，其中 ρ 是密度，c 是该材料中的声速。Z 的差异越大，反射的比例越大。这正是超声成像的基础。
Frequency: higher frequencies give better resolution (shorter wavelength) but less penetration depth.
频率：频率越高分辨率越高（波长越短），但穿透深度越小。
6. Ultrasound in Medicine | 超声波在医学中的应用
An ultrasound transducer (probe) contains piezoelectric crystals that both emit and detect ultrasound. In pulse‑echo mode, the probe sends short pulses into the body and listens for echoes reflected from boundaries. The time delay between emission and echo is used to calculate depth, because distance = speed × time / 2 (the wave travels there and back).
Prenatal scanning – to check fetal development, measure size, detect abnormalities. A gel is applied to the skin to eliminate air gaps (air would reflect almost all the ultrasound).
Echocardiography – imaging the heart in real time, measuring blood flow using the Doppler effect.
超声心动图——实时心脏成像，利用多普勒效应测量血流。
Breaking up kidney stones (lithotripsy) – high‑intensity focused ultrasound (HIFU) pulverises the stones without surgery.
粉碎肾结石（碎石术）——高强度聚焦超声 (HIFU) 无需手术即可粉碎结石。
Physiotherapy – ultrasound heating can increase blood flow and aid tissue repair.
物理治疗——超声加热可增加血流，促进组织修复。
Advantages: safe, real‑time, portable, relatively cheap, no ionising radiation. Disadvantage: cannot penetrate bone or gas‑filled cavities well, lower resolution compared to CT or MRI.
Endoscopy allows direct visual inspection inside the body using an endoscope – a flexible tube containing two bundles of optical fibres. One bundle carries light down into the patient (illumination), while the other carries an image back to a camera or eyepiece. Keyhole surgery can be performed by passing small instruments through the endoscope.
Optical fibres work by total internal reflection. Light is guided along the fibre because the core has a higher refractive index than the cladding, and the light hits the boundary at angles greater than the critical angle. As long as the fibre is not bent too sharply, very little light escapes. This allows bright, clear images from deep inside the body.
Endoscopy uses non‑ionising radiation (visible light) and is completely safe in terms of radiation, but invasive and carries infection risks.
内窥镜使用非电离辐射（可见光），在辐射方面完全安全，但属侵入性操作，存在感染风险。
8. Nuclear Medicine and Tracers | 核医学与示踪剂
Nuclear medicine uses radioactive isotopes injected into the body to diagnose or treat disease. A small amount of a radioactive tracer – often technetium‑99m, which emits gamma rays and has a short half‑life of 6 hours – is taken up by specific organs. A gamma camera detects the gamma rays and builds an image showing the concentration of the tracer. Because the patient is the source of radiation, the detector is placed outside and does not rotate like a CT.
PET (Positron Emission Tomography) scanners use tracers that emit positrons (e.g. fluorine‑18). A positron annihilates with an electron, producing two gamma photons travelling in opposite directions, which are detected simultaneously. This gives very detailed 3D functional images, often combined with CT (PET‑CT) for anatomical information.
Radiotherapy uses high‑energy radiation (gamma rays from cobalt‑60 or X‑rays from a linear accelerator) to destroy cancer cells. Careful planning is needed to maximise dose to the tumour while sparing healthy tissue. Brachytherapy places a small radioactive source directly inside or next to the tumour.
放射治疗利用高能辐射（钴‑60 的伽马射线或直线加速器产生的 X 射线）来摧毁癌细胞。需要精心规划，使肿瘤剂量最大化同时保护健康组织。近距离放射治疗将小型放射源直接放置在肿瘤内部或旁边。
9. Comparing Medical Imaging Techniques | 医学成像技术比较
OCR IGCSE often asks you to compare methods based on: type of waves used, ionising or not, resolution, safety, cost and typical uses. A table is an excellent way to organise this information.
You must also be able to explain why ultrasound is preferred for pregnancy scans (no ionising radiation) and why CT is used for emergency brain scans (rapid, high‑resolution 3D).
你还必须能解释为什么超声被优先用于孕检（无电离辐射），以及为什么 CT 用于急诊脑部扫描（快速、高分辨率 3D 图像）。
10. Key Equations and Calculations | 关键公式与计算
Although medical physics is often descriptive, there are a few crucial equations you should be able to use. These frequently appear in OCR IGCSE calculation questions.
For ultrasound, if you know the frequency and the speed of sound in tissue (∼1540 m s⁻¹), you can calculate wavelength. This helps explain why higher frequency gives better resolution.
对于超声波，若已知频率和人体组织中的声速（约 1540 m s⁻¹），可算出波长。这有助于解释为何更高频率能带来更好的分辨率。
Distance calculation in pulse‑echo: d = (v × t) / 2
Here t is the time between sending the pulse and receiving the echo. The division by 2 accounts for the round trip. Example: If a pulse takes 20 μs to return and v = 1500 m s⁻¹, depth = (1500 × 20×10⁻⁶) / 2 = 0.015 m = 1.5 cm.
这里 t 是发射脉冲到接收回波的时间间隔。除以 2 是因为往返路程。例：若脉冲回波用时 20 μs，v = 1500 m s⁻¹，深度 = (1500 × 20×10⁻⁶) ÷ 2 = 0.015 m = 1.5 cm。
Critical angle for optical fibres: sin c = n₂ / n₁
Where n₁ is the core refractive index and n₂ is the cladding index (n₁ > n₂). Total internal reflection occurs only when the angle of incidence > c.
其中 n₁ 为纤芯折射率，n₂ 为包层折射率 (n₁ > n₂)。仅当入射角 > c 时发生全内反射。
Half‑life and activity: A = A₀ (½)^(t / T½)
This describes the decay of a radioactive tracer. You may need to calculate how much remains after a certain time, or determine a suitable isotope based on its half‑life so that it has a low activity when excreted.
In radiotherapy questions, mention that ionising radiation damages DNA, and that the beam is rotated around the patient to minimise damage to healthy tissue.
OCR multiple‑choice questions frequently test the distinction between X‑rays and ultrasound, the role of piezoelectric crystals, and how half‑life affects the choice of tracer. Practice these repeatedly.
OCR 单选题经常考查 X 射线与超声波的区别、压电晶体的作用，以及半衰期如何影响示踪剂的选择。请反复练习。
12. Summary | 总结
Medical physics is the perfect blend of core physics ideas and real‑world application. Remember: X‑rays and CT use ionising EM waves and provide excellent resolution but carry a radiation risk. Ultrasound uses non‑ionising sound waves and is safe for repeated scanning, but resolution is lower. Endoscopy gives direct optical images with no radiation, while nuclear medicine provides functional information using radioactive tracers. For the OCR IGCSE exam, your ability to compare these techniques with clarity and accuracy will earn you top marks.
This revision guide summarises the essential concepts, equations, and common pitfalls for IGCSE Edexcel Physics. Each section is presented as a quick-fire set of notes to help you consolidate your knowledge right before the exam.
Speed is the rate of change of distance; velocity is speed in a given direction. Acceleration is the rate of change of velocity.
速率是距离的变化率；速度是给定方向上的速率。加速度是速度的变化率。
v = d ÷ t a = (v – u) ÷ t
Newton’s second law states that net force equals mass times acceleration. An object will accelerate only if the resultant force acting on it is not zero.
牛顿第二定律指出，合力等于质量乘以加速度。只有当作用在物体上的合力不为零时，物体才会加速。
F = m × a
For motion in a straight line, you can use the equations of uniformly accelerated motion. Remember to choose the appropriate sign for direction.
对于直线运动，你可以使用匀加速运动方程。记得为方向选择合适的正负号。
v = u + at v² = u² + 2as s = ut + ½at²
Momentum is the product of mass and velocity, and it is conserved in collisions and explosions as long as no external forces act.
动量是质量与速度的乘积，在没有外力作用的情况下，它在碰撞和爆炸中守恒。
p = m × v Total p before = Total p after
Force can also be defined as the rate of change of momentum. A larger force results in a quicker change in momentum.
力也可以定义为动量的变化率。力越大，动量变化越快。
2. Energy, Work and Power | 能量、功和功率
Work done is the energy transferred when a force moves an object through a distance. The unit of work and energy is the joule (J).
功是力使物体移动一段距离时转移的能量。功和能量的单位是焦耳 (J)。
W = F × d (when force and displacement are parallel)
Gravitational potential energy is the energy an object possesses due to its height above the ground. Kinetic energy depends on mass and speed squared.
重力势能是物体因其离地高度而具有的能量。动能取决于质量和速度的平方。
GPE = m × g × h KE = ½ × m × v²
Energy is always conserved; it can be transferred or stored, but never destroyed. In real systems, some energy is dissipated as thermal energy.
能量始终守恒；它可以转移或储存，但绝不会被消灭。在实际系统中，部分能量会以热能形式耗散。
Power is the rate of doing work or the rate of energy transfer. It is measured in watts (W).
功率是做功的快慢或能量转移的速率。它以瓦特 (W) 为单位。
P = W ÷ t P = E ÷ t
Efficiency compares useful output energy to total input energy. No device can be 100% efficient due to unavoidable energy losses.
效率用于比较有用输出能量与总输入能量。由于不可避免的能量损失，任何设备的效率都无法达到100%。
Efficiency = (Useful energy output ÷ Total energy input) × 100%
3. Thermal Physics | 热物理学
Temperature is a measure of the average kinetic energy of particles. Heat is the transfer of thermal energy from a hotter object to a colder one.
温度是粒子平均动能的量度。热量是从较热物体向较冷物体传递的热能。
Conduction is the transfer of heat through a solid by particle vibrations and free electron movement. Metals are good conductors.
热传导是通过粒子振动和自由电子运动在固体中传递热量。金属是良导体。
Convection occurs in fluids (liquids and gases) when warmer, less dense regions rise and cooler, denser regions sink, setting up a convection current.
对流发生在流体（液体和气体）中，较暖、密度较小的区域上升，较冷、密度较大的区域下沉，从而形成对流。
Radiation is the transfer of energy by infrared electromagnetic waves; it does not require a medium and can travel through a vacuum.
辐射是通过红外电磁波传递能量；它不需要介质，可以在真空中传播。
During a change of state (melting, boiling, condensing, freezing), the temperature remains constant even though energy is being transferred. The specific latent heat is the energy required to change the state of 1 kg of a substance without changing its temperature.
The specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 °C.
比热容是使1千克物质温度升高1°C所需的能量。
ΔE = m × c × Δθ
4. Waves | 波
Waves transfer energy without transferring matter. In transverse waves, oscillations are perpendicular to the direction of energy travel; in longitudinal waves, oscillations are parallel.
波传递能量而不传递物质。在横波中，振动方向与能量传播方向垂直；在纵波中，振动方向平行。
Amplitude is the maximum displacement from the rest position. Wavelength is the distance between two consecutive points in phase, e.g. crest to crest.
振幅是偏离平衡位置的最大位移。波长是相邻两个同相点之间的距离，例如波峰到波峰。
Frequency is the number of complete waves passing a point per second, measured in hertz (Hz). The wave equation links speed, frequency and wavelength.
频率是每秒通过某点的完整波的数量，以赫兹 (Hz) 为单位。波动方程联系了波速、频率和波长。
v = f × λ
Reflection of waves follows the law of reflection: angle of incidence equals angle of reflection. Refraction occurs when waves change speed as they cross a boundary, causing a change in direction unless they strike along the normal.
Diffraction is the spreading out of waves when they pass through a gap or around an obstacle. The effect is most noticeable when the gap width is similar to the wavelength.
衍射是波通过狭缝或绕过障碍物时扩散的现象。当缝隙宽度与波长相近时，衍射效果最明显。
5. Light and Sound | 光与声
Light is a transverse electromagnetic wave that travels at approximately 3 × 10⁸ m/s in a vacuum. Sound is a longitudinal mechanical wave requiring a medium; it travels fastest in solids, slower in liquids, and slowest in gases.
The law of reflection applies to light. In a plane mirror, the image is virtual, upright, laterally inverted, and the same size as the object.
反射定律适用于光。在平面镜中，像是虚像、正立、横向反转且与物体等大。
Refraction of light is governed by Snell’s law. The refractive index of a medium is the ratio of the speed of light in a vacuum to the speed in the medium.
光的折射遵循斯涅尔定律。介质的折射率是光在真空中的速度与在介质中速度的比值。
n = sin i ÷ sin r n = c ÷ v
Total internal reflection occurs when light travels from a denser to a less dense medium at an angle of incidence greater than the critical angle. The critical angle is given by sin c = 1/n.
当光从光密介质射向光疏介质且入射角大于临界角时，会发生全内反射。临界角由 sin c = 1/n 给出。
Sound waves can be reflected (echoes), refracted, and diffracted. The pitch of a sound depends on frequency; loudness depends on amplitude.
声波可以反射（回声）、折射和衍射。音调取决于频率；响度取决于振幅。
Ultrasound is sound with frequency above 20 kHz. It is used in sonar, medical imaging, and cleaning because of its ability to be partially reflected at boundaries between different tissues or materials.
Current is the rate of flow of charge. Conventional current flows from positive to negative, opposite to electron flow.
电流是电荷流动的速率。常规电流方向是从正极到负极，与电子流动方向相反。
I = Q ÷ t
Voltage (potential difference) is the energy transferred per unit charge. Resistance opposes current flow and is measured in ohms (Ω).
电压（电势差）是每单位电荷转移的能量。电阻阻碍电流流动，以欧姆 (Ω) 为单位。
V = W ÷ Q V = I × R
In a series circuit, current is the same everywhere, and the total resistance is the sum of individual resistances. The supply voltage is shared across components.
在串联电路中，各处电流相等，总电阻为各电阻之和。电源电压在各元件间分配。
In a parallel circuit, the voltage across each branch is the same. The total current is the sum of the currents in the branches; the total resistance is less than the smallest individual resistance.
在并联电路中，各支路两端电压相等。总电流等于各支路电流之和；总电阻小于最小的单个电阻。
Electrical power is the rate at which electrical energy is transferred. It can be expressed in terms of current and voltage, or current and resistance.
电功率是电能转移的速率。它可以用电流和电压，或电流和电阻来表示。
P = I × V P = I² × R
Energy transferred by an appliance depends on power and time. The kilowatt-hour (kWh) is a unit of energy commonly used for domestic electricity consumption.
用电器转移的能量取决于功率和时间。千瓦时 (kWh) 是家庭用电常用的能量单位。
E = P × t E = I × V × t
7. Magnetism and Electromagnetism | 磁学和电磁学
Magnets have north and south poles. Like poles repel; unlike poles attract. A magnetic field line shows the direction a north pole would move; it points from north to south.
磁铁有北极和南极。同极相斥；异极相吸。磁力线表示北极移动的方向，从北极指向南极。
An electric current produces a circular magnetic field around a straight wire. Wrapping the wire into a solenoid concentrates the field, creating a strong, uniform field inside, similar to a bar magnet.
电流在直导线周围产生环形磁场。将导线绕成螺线管可集中磁场，内部产生类似条形磁铁的强而均匀的磁场。
Electromagnets are solenoids with an iron core, which greatly increases the magnetic field strength. They can be switched on and off, and are used in relays, electric bells, and lifting magnets.
电磁铁是带有铁芯的螺线管，铁芯大大增强了磁场强度。它们可以开关，用于继电器、电铃和起重磁铁。
The motor effect: a current-carrying conductor in a magnetic field experiences a force. Fleming’s left-hand rule predicts the direction of force (thuMb – Motion, First finger – Field, seCond finger – Current).
Electromagnetic induction: when a conductor cuts magnetic field lines, a potential difference (emf) is induced. The effect is increased by moving the conductor faster, using a stronger magnet, or adding more turns to a coil.
Transformers change the size of an alternating voltage. A step-up transformer increases voltage and decreases current; a step-down transformer does the opposite.
变压器可以改变交流电压的大小。升压变压器升高电压、降低电流；降压变压器则相反。
Vₚ ÷ Vₛ = Nₚ ÷ Nₛ Vₚ × Iₚ = Vₛ × Iₛ (ideal)
8. Atomic Physics and Radioactivity | 原子物理与放射性
Atoms consist of a small, dense nucleus containing protons and neutrons, surrounded by electrons in energy levels. The nucleus is held together by the strong nuclear force.
原子由包含质子和中子的致密小原子核以及处于能级中的电子组成。原子核由强核力束缚在一起。
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. Their chemical properties are identical, but some isotopes are radioactive.
同位素是质子数相同但中子数不同的同种元素的原子。它们的化学性质相同，但有些同位素具有放射性。
Radioactive decay is a random process where unstable nuclei emit alpha, beta, or gamma radiation. Alpha particles are helium nuclei, beta particles are fast electrons, and gamma rays are electromagnetic waves.
Activity is the number of decays per second, measured in becquerels (Bq). Half-life is the average time taken for the activity of a radioactive source to halve.
活度是每秒衰变次数，以贝克勒尔 (Bq) 为单位。半衰期是放射源活度减半所需的平均时间。
Background radiation comes from natural sources such as radon gas, cosmic rays, and rocks, as well as artificial sources. The dose received is measured in sieverts (Sv).
背景辐射来自天然源，如氡气、宇宙射线和岩石，以及人造源。接收的剂量以希沃特 (Sv) 为单位。
Uses of radiation include sterilising equipment (gamma), smoke detectors (alpha), thickness gauging (beta), and medical tracers (gamma or beta with short half-lives). Safety precautions include distance, shielding, and limiting exposure time.
Nuclear fission is the splitting of a large nucleus (e.g., uranium-235) after absorbing a neutron, releasing energy and more neutrons. Nuclear fusion is the joining of light nuclei (e.g., hydrogen) to form a heavier nucleus, releasing even more energy.
The Solar System consists of the Sun, eight planets, their moons, and smaller bodies such as asteroids and comets. Planets orbit the Sun in elliptical paths.
太阳系由太阳、八大行星、它们的卫星以及小行星和彗星等较小天体组成。行星以椭圆轨道绕太阳运行。
Gravitational force provides the centripetal force that keeps planets and satellites in orbit. The orbital speed of a planet decreases with increasing distance from the Sun.
引力提供维持行星和卫星沿轨道运行的向心力。行星的轨道速度随与太阳距离的增加而减小。
v = 2πr ÷ T
A galaxy is a vast collection of billions of stars, gas, and dust. The Milky Way is our galaxy. The Universe contains billions of galaxies, and it began with the Big Bang about 13.8 billion years ago.
Evidence for the Big Bang includes the redshift of light from distant galaxies, showing they are moving away, and the cosmic microwave background radiation. The greater the redshift, the faster a galaxy is receding.
Memorise the main equations, but also understand how to rearrange them. The table below summarises the most frequently examined relationships.
记住主要方程，但也要理解如何移项。下表总结了最常考查的关系。
Quantity
Equation
Units
Speed
v = d ÷ t
m/s
Acceleration
a = (v – u) ÷ t
m/s²
Force
F = m × a
N
Momentum
p = m × v
kg m/s
Kinetic Energy
KE = ½ m v²
J
Work Done
W = F × d
J
Power
P = E ÷ t
W
Electrical Power
P = I × V
W
Ohm’s Law
V = I × R
V, A, Ω
Wave Speed
v = f × λ
m/s
Transformer
Vₚ / Vₛ = Nₚ / Nₛ
–
Always show your working, include units, and check the number of significant figures. For calculation questions, begin by writing the formula, then substitute values before calculating the answer.
始终展示解题步骤，注明单位，并检查有效数字。对于计算题，先写出公式，然后代入数值再算出答案。
In practical-based questions, be ready to describe how to reduce errors (e.g., repeating measurements, using fiducial markers, checking zero errors).
在实验类题目中，准备好描述如何减少误差（例如，重复测量、使用基准标记、检查零误差）。
Published by TutorHao | Physics Revision Series | aleveler.com
Understanding resistance is essential for mastering electric circuits in the IGCSE WJEC Physics syllabus. This article covers all the key concepts, from the definition of resistance and Ohm’s law to the factors that affect it, how resistors combine, and the behaviour of special components like thermistors and LDRs. Each section presents paired English and Chinese explanations to support both language learners and international students.
Resistance is a measure of how much a component opposes the flow of electric current. The greater the resistance, the smaller the current for a given potential difference. Resistance is caused by collisions between the free electrons moving through a conductor and the vibrating positive ions of the metal lattice.
Resistance is defined by the equation R = V / I, where R is the resistance in ohms (Ω), V is the potential difference in volts (V), and I is the current in amperes (A). One ohm is the resistance when a potential difference of one volt produces a current of one ampere.
电阻的定义式为 R = V / I，其中 R 是电阻（单位：欧姆 Ω），V 是电势差（单位：伏特 V），I 是电流（单位：安培 A）。当一伏特的电压使电路中产生一安培的电流时，该元件的电阻就是一欧姆。
Conductance is the reciprocal of resistance, but for IGCSE, the focus is always on resistance and how it limits current. Good conductors have very low resistance, while insulators have extremely high resistance.
Ohm’s law states that for a metallic conductor at constant temperature, the current through it is directly proportional to the potential difference across it. This relationship is written as V = I × R, or rearranged as I = V / R.
欧姆定律指出，对于恒温下的金属导体，通过它的电流与导体两端的电势差成正比。这个关系写作 V = I × R，或变形为 I = V / R。
A component that obeys Ohm’s law is called an ohmic conductor. Its current–voltage (I–V) graph is a straight line passing through the origin, showing a constant resistance. However, many components, such as filaments and semiconductors, do not follow Ohm’s law under all conditions; these are non‑ohmic conductors.
Always remember that Ohm’s law is only valid if temperature (and other physical conditions) remain constant. When current increases and heats up the wire, the resistance changes, and the I–V graph curves.
The resistance of a wire depends on four main factors: length, cross‑sectional area, the material itself, and temperature. Understanding these factors helps in designing circuits and choosing the right components.
Length (L): Resistance is directly proportional to the length of the conductor. If the length doubles, the resistance doubles, because the electrons must travel twice as far and encounter twice as many collisions with ions.
Cross‑sectional area (A): Resistance is inversely proportional to the area. A thicker wire has more space for the electrons to flow, so the resistance is lower. If the area doubles, the resistance halves.
Material: Every material has a characteristic resistivity (ρ). Good conductors like copper have very low resistivity, while alloys like nichrome have higher resistivity, making them useful for heating elements.
Temperature: For a metallic conductor, resistance increases with temperature. Heating causes the positive ions in the lattice to vibrate more vigorously, increasing the frequency of collisions and making it harder for electrons to pass through. For semiconductors and thermistors, resistance typically decreases as temperature rises.
4. Resistivity and the Resistance Formula | 电阻率与电阻公式
The resistance of a uniform conductor can be calculated using the formula R = ρL / A, where ρ is the resistivity of the material in ohm‑metres (Ω⋅m), L is the length in metres (m), and A is the cross‑sectional area in square metres (m²).
均匀导体的电阻可用公式 R = ρL / A 计算，其中 ρ 是材料的电阻率（单位：欧姆·米 Ω⋅m），L 是长度（单位：米 m），A 是横截面积（单位：平方米 m²）。
Resistivity is a property of the material itself and does not depend on the dimensions of the sample. For IGCSE WJEC, you are not required to perform complex calculations with resistivity, but you should understand the proportionalities: R ∝ L and R ∝ 1/A.
电阻率是材料本身的属性，与试样的尺寸无关。IGCSE WJEC 不要求进行复杂的电阻率计算，但你需要理解比例关系：R ∝ L 和 R ∝ 1/A。
This formula explains why long, thin wires have high resistance, and short, thick wires have low resistance. It also shows why you should use thick cables for high‑current appliances to reduce energy lost as heat.
When resistors are connected in series, the same current passes through each resistor, but the total potential difference is shared across them. The total (equivalent) resistance Rtotal is simply the sum of the individual resistances.
Adding more resistors in series always increases the total resistance because the current must flow through each one in turn, and the conducting path becomes effectively longer.
串联更多的电阻总会使总电阻增加，因为电流必须依次流过每一个电阻，导电通路相当于变长了。
Series circuits are often used when you want to share voltage, for example in potential divider circuits or when connecting several low‑voltage bulbs to a higher‑voltage supply, provided the currents match.
When resistors are connected in parallel, the potential difference across each resistor is the same, but the total current is divided among the branches. The reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances.
电阻并联时，每个电阻两端的电压相同，但总电流分配于各支路。总电阻的倒数等于各电阻倒数之和。
1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + …
For the special case of two parallel resistors, the total resistance can be found using the product‑over‑sum formula: Rtotal = (R₁ × R₂) / (R₁ + R₂). However, it is safer to use the reciprocal formula to avoid mistakes, especially with three or more resistors.
Adding more resistors in parallel decreases the total resistance because additional paths are created for the current. The total resistance of a parallel combination is always less than the smallest individual resistance.
并联更多电阻会降低总电阻，因为为电流提供了额外的通路。并联组合的总电阻始终小于其中最小的单个电阻。
7. Current–Voltage Characteristics | 电流–电压特性
The I–V characteristic of a component is a graph showing how the current through it varies with the applied potential difference. The shape of the graph reveals whether the component is ohmic or non‑ohmic, and how its resistance changes.
Ohmic conductor (e.g., a metal wire at constant temperature): straight line through origin, constant gradient. Resistance is constant, equal to 1/gradient.
欧姆导体（如恒温下的金属导线）：过原点的直线，斜率恒定。电阻恒定，等于斜率的倒数。
Filament lamp: as the current increases, the wire heats up, and resistance rises. The I–V graph curves, with a decreasing gradient. At higher voltages, the line becomes less steep, showing a larger resistance.
Diode: a diode allows current in one direction only. The forward I–V graph shows almost no current until the threshold voltage (≈0.6 V for silicon) is reached, after which current rises steeply. In the reverse direction, current is negligible (except at very high reverse breakdown).
You should be able to sketch and interpret these graphs and link the shape to resistance changes. In a filament lamp, the gradient at any point gives the reciprocal of the resistance at that voltage.
8. Variable Resistors and Potentiometers | 可变电阻与电位器
A variable resistor (rheostat) allows you to change the resistance in a circuit manually. It typically consists of a coil of resistance wire and a sliding contact. Moving the slider changes the length of wire in the circuit, thus varying the resistance.
Variable resistors are used for dimming lights, controlling volume, adjusting motor speed, and acting as potential dividers. In a potential divider arrangement, the variable resistor is connected across a fixed voltage, and the output is taken between the wiper and one end.
At IGCSE level, you should be able to explain how turning a knob or sliding a contact alters the balance of voltage across components and how this can make a lamp brighter or dimmer.
A thermistor is a temperature‑dependent resistor. There are two types: negative temperature coefficient (NTC) thermistors, whose resistance decreases as temperature rises, and positive temperature coefficient (PTC) thermistors, whose resistance increases with temperature. NTC thermistors are the most commonly examined.
In a typical sensing circuit, a thermistor is placed in a potential divider with a fixed resistor. When the temperature changes, the share of the voltage across the thermistor also changes. This voltage can be used to trigger an alarm or switch a heating system on or off.
NTC thermistors are widely used in electronic thermometers, fire alarms, and temperature‑controlled circuits. The graph of resistance against temperature is a curve that drops steeply at lower temperatures and flattens out as temperature rises further.
A light‑dependent resistor (LDR) changes its resistance based on the intensity of light falling on it. In darkness, an LDR has a very high resistance (often several megaohms); in bright light, its resistance drops significantly (to a few hundred ohms or less).
LDRs are made from semiconductor materials such as cadmium sulphide. When photons hit the semiconductor, they provide enough energy to release more charge carriers, so conductance increases and resistance falls.
Typical applications include street lights that switch on automatically at dusk, burglar alarm sensors, and camera light meters. In a potential divider circuit with a fixed resistor, the voltage across the LDR changes according to the light level, which can then control a transistor or relay.
Investigating the resistance of a wire: You will often be asked to describe an experiment to find how the resistance of a wire depends on its length or thickness. Set up a circuit with a power supply, an ammeter in series, and a voltmeter in parallel with the wire under test. Vary the length (by moving a crocodile clip) or use different diameters, record V and I, and calculate R = V/I for each trial. Keep the current small to minimise heating effects.
探究导线电阻：常被要求描述一个实验，以找出导线电阻如何随长度或粗细变化。连接一个包含电源、串联电流表和并联在待测导线两端电压表的电路。通过移动鳄鱼夹改变长度，或使用不同直径的导线，记录 V 和 I，对每次测试计算 R = V/I。保持电流较小，以减小发热影响。
Plotting a graph of R against L should yield a straight line through the origin if temperature is constant, confirming R ∝ L. A graph of R against 1/A should also be linear, confirming R ∝ 1/A.
若温度恒定，绘制 R–L 图应得到一条过原点的直线，证实 R ∝ L。绘制 R–1/A 图也应呈线性，证实 R ∝ 1/A。
Investigating I–V characteristics: Use a similar setup but include a variable resistor or potential divider to vary the applied voltage smoothly. Take readings for both directions (reverse the connections) for a diode. For a filament lamp, increase voltage in small steps, allowing the lamp to warm up.
12. Key Points and Common Misconceptions | 重点与常见误区
Resistance is not constant for all components. Only ohmic conductors have constant resistance. Filaments, diodes, thermistors, and LDRs change their resistance under different conditions. / 并非所有元件的电阻都是定值。 只有欧姆导体具有恒定电阻。灯丝、二极管、热敏电阻和 LDR 在不同条件下电阻会改变。
Temperature effect: In metals, resistance increases with temperature. In thermistors (NTC), resistance decreases with temperature. Do not confuse the two. / 温度效应： 金属中，电阻随温度升高而增大；而 NTC 热敏电阻的电阻随温度升高而减小。切勿混淆两者。
Series vs parallel: Series increases total resistance; parallel decreases total resistance. The parallel equivalent is always less than the smallest branch resistor. / 串联与并联： 串联增大总电阻；并联减小总电阻。并联等效电阻永远小于最小的支路电阻。
LDR and thermistor applications usually involve a potential divider, not just the sensor alone. The output voltage is taken from either the sensor or the fixed resistor, depending on whether you want voltage to rise or fall with the physical change. / LDR 与热敏电阻的应用 通常涉及分压器，而非单独使用传感器。根据你希望输出电压随物理量升高还是降低，可以从传感器或固定电阻两端取输出。
Ohm’s law V = I × R is always true for defining resistance, but the condition I ∝ V only holds when resistance is constant. / 欧姆定律 V = I × R 始终可用于定义电阻，但只有电阻恒定时 I ∝ V 才成立。
By mastering these concepts, you will be well prepared for both calculation questions and descriptive answers on resistance in the WJEC IGCSE Physics exam. Practice drawing diagrams and explaining the behaviour of components clearly and concisely.
Long-answer and essay-style questions in OCR GCSE Physics challenge you to demonstrate depth of understanding, logical reasoning, and effective communication. This template will equip you with a reliable framework to structure your responses, whether you are explaining a concept, describing an experiment, or evaluating data. Follow the steps below to ensure your essays are clear, concise, and scientifically rigorous.
Before you begin writing, carefully read the question and underline the command words (e.g., ‘describe’, ‘explain’, ‘evaluate’, ‘compare’). Identify the key scientific terms and note the mark allocation. A 6-mark question may require multiple points and a clear structure, whereas a 2-mark explanation needs concise precision. Understanding exactly what the examiner wants prevents irrelevant content.
Spend 2-3 minutes jotting down a brief outline. List the main ideas in a logical order, separating them into introduction, body, and conclusion. For longer essays, use a mind map or bullet points. A well-planned answer flows better and ensures you cover all assessment objectives (AO1 knowledge, AO2 application, AO3 analysis).
Start with a sentence that defines the key concept or outlines the scope of your answer. For example: ‘The principle of moments states that for an object in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.’ Follow with a brief statement of what your essay will discuss. Avoid repeating the question verbatim.
Each body paragraph should follow the PEEL structure: Point – state the idea clearly; Evidence – provide a scientific fact, formula, or data; Explanation – use physics reasoning to explain why or how; Link – connect back to the question or to the next paragraph. This ensures every sentence contributes to the argument.
Example of a PEEL paragraph in Physics: Point: Increasing the resistance in a circuit reduces the current. Evidence: Ohm’s law states V = IR. Explanation: For a fixed voltage, if R is larger, I must be smaller because I = V/R. Link: This explains why adding more resistors in series dims the bulbs in a circuit.
When explaining a concept, use precise terminology and break down the process step by step. For instance, to explain Brownian motion, describe the random movement of smoke particles caused by collisions with invisible air molecules. Reference kinetic theory, energy transfer, or forces as appropriate. Avoid vague statements like ‘it moves randomly’ without giving the scientific reason.
If the essay involves quantitative physics, you must state the formula, substitute values correctly, and show the result with units. Use the standard format: write the equation in symbols, then substitution, then answer. For example:
v² = u² + 2as → 0 = (20)² + 2 × a × 50 → a = −4 m/s²
Make sure to include the unit and interpret the result, e.g., the negative sign indicates deceleration. Never forget to state the equation before using numbers, as this demonstrates knowledge (AO1).
When outlining an experiment, structure your answer as: Aim – what you are investigating; Equipment – list essential apparatus; Method – stepwise procedure, including control variables and measurements; Expected results – qualitative or quantitative outcome; Safety – hazards and precautions. For example, to determine the density of an irregular solid, describe using a displacement can and balance.
If you draw a diagram or refer to given data, label it clearly and use it to support your explanation. Mention trends, gradients, or intercepts when analysing graphs. Use phrases like ‘as the independent variable increases, the dependent variable decreases linearly, showing an inverse relationship.’ This shows analytical skills (AO3).
Your conclusion should summarise the main points and directly answer the question. Do not introduce new information. If the question asks you to evaluate, give a balanced judgement (e.g., ‘The experiment was reliable because repeats showed consistent results, but the resolution of the thermometer limited accuracy.’). A strong conclusion ties all your arguments together.
Not reading the question fully: Always check for multiple part questions or specific command words. Missing scientific details: Use correct units, symbols, and terminology. Poor time allocation: Don’t spend too long on one essay and neglect others. Too much narrative, too little physics: Every sentence must serve the scientific argument.
Another frequent mistake is using everyday language instead of scientific vocabulary. Words like ‘push’ should be replaced by ‘force’, ‘speed’ by ‘velocity’ where appropriate, and ‘heat’ by ‘thermal energy’. Also, always include units in final answers and refer to them when analysing results.
In an exam, quickly scan the paper and assign time based on marks. For a 6-mark essay, aim to spend 8-10 minutes: 1 minute planning, 5-6 minutes writing, 2 minutes reviewing. Keep an eye on the clock. If you run out of time, bullet points can still secure some marks if they contain key scientific points.
Introduction: A transformer is a device that changes the voltage of an alternating current. It consists of two coils wound on a soft iron core. The national grid uses step-up and step-down transformers to efficiently transmit electrical power over long distances.
Body 1 – Working principle: An alternating current in the primary coil produces a changing magnetic field in the iron core. This changing field induces an alternating voltage in the secondary coil via electromagnetic induction. The voltage ratio equals the turns ratio: Vₚ/V
Published by TutorHao | IGCSE Physics Revision Series | aleveler.com
Circular motion sits at the heart of the OCR A-Level Physics mechanics module. From satellites orbiting a planet to a car rounding a banked curve, the same few principles govern any object moving along a circular arc. Mastering radian measure, angular velocity, centripetal acceleration and the deceptively tricky distinction between centripetal and centrifugal forces is essential for tackling both structured questions and synoptic challenges. This guide walks you through every key concept with tightly paired English–Chinese explanations, clear diagrams in words and plenty of equation summaries so that you can approach the exam with real confidence.
1. Radian Measure and Angular Displacement | 弧度制与角位移
An angle of one radian is defined as the angle subtended at the centre of a circle by an arc whose length equals the radius: θ (rad) = arc length / radius = s/r. Because the circumference of a full circle is 2πr, 360° is exactly 2π radians. Radian measure is dimensionless but must be used in all angular equations at A-Level, making conversions between degrees and radians second nature.
Common angles to remember: 180° = π rad, 90° = π/2 rad, 60° = π/3 rad, 45° = π/4 rad, 30° = π/6 rad. Angular displacement Δθ is simply the angle through which a point on the rotating object has moved, usually measured in radians.
Angular velocity ω (omega) is the rate of change of angular displacement: ω = Δθ / Δt. Its SI unit is radians per second (rad s⁻¹). For uniform circular motion, ω is constant. The time taken for one complete revolution is the period T, and the number of revolutions per second is the frequency f (Hz). The key relationships are: ω = 2π / T and ω = 2π f. These formulas are vital for switching between time-based and angle-based descriptions.
Many exam questions provide the period or frequency and expect you to find the angular velocity before calculating acceleration or force. Always check whether a question gives rpm (revolutions per minute); convert to Hz by dividing by 60, then use ω = 2π f.
许多考题会直接给出周期或频率，要求你先求出角速度，再进一步计算加速度或力。务必注意题目中是否给出的是rpm（每分钟转数）；需要先除以60转化为Hz，再使用 ω = 2π f 计算。
3. Relating Linear and Angular Quantities | 线量与角量的关系
The linear speed v of a point moving along a circular path is related to the angular velocity by v = ω r, where r is the radius of the circle. This arises from the definition of radian measure: s = r θ, so v = s/t = r θ/t = r ω. Even if the angular speed is constant, the velocity vector is continually changing direction, which is why an acceleration is present.
沿圆周运动的质点，其线速度 v 与角速度之间的关系为 v = ω r，其中 r 为圆半径。这一关系来源于弧度制的定义：s = r θ，因此 v = s/t = r θ/t = r ω。即使角速度恒定，速度矢量的方向也在不断变化，这就导致了加速度的存在。
Conversely, angular velocity can be expressed as ω = v / r. This is particularly useful when comparing two points on a rotating rigid body: points farther from the axis have a larger linear speed but the same angular velocity. Always ensure that ω is in rad s⁻¹ when using v = ω r.
反过来也可将角速度写成 ω = v / r。这在比较旋转刚体上不同点的运动时特别有用：离转轴越远的点线速度越大，但角速度相同。使用 v = ω r 时务必保证 ω 的单位是 rad s⁻¹。
4. Centripetal Acceleration | 向心加速度
For an object in uniform circular motion, the magnitude of the acceleration towards the centre—the centripetal acceleration—is given by two interchangeable expressions:
a = v² / r and a = ω² r
匀速圆周运动中，指向圆心的加速度——向心加速度——的大小由两个等价的表达式给出：a = v² / r 与 a = ω² r。
The direction of this acceleration is always towards the centre of the circle, perpendicular to the instantaneous velocity. Although the speed may be constant, the velocity changes direction, so there is a resultant acceleration. This is not an acceleration that changes the magnitude of the velocity but one that changes its direction. Understanding this vector nature is crucial for applying Newton’s second law correctly.
According to Newton’s second law, an object experiencing an acceleration must be acted upon by a net force. The force that keeps an object moving in a circle is the centripetal force, F = m a, directed towards the centre. Its magnitude can be written as:
F = m v² / r or F = m ω² r
根据牛顿第二定律，存在加速度的物体必然受到净力的作用。使物体维持圆周运动的力就是向心力 F = m a，方向指向圆心。其大小可表示为：F = m v² / r 或 F = m ω² r。
Centripetal force is not a new type of force; it is simply the name given to the resultant force directed towards the centre of the circle. It can be provided by tension, gravity, friction, the normal reaction or a combination of these. For example, when a car corners on a flat road, the centripetal force is the static friction between the tyres and the road. In an orbit, gravity supplies the centripetal demand.
6. Common Misconceptions: Centrifugal Force | 常见误区：离心力
A persistent error is the belief in a real outward ‘centrifugal’ force acting on a circling object. In an inertial frame of reference (a non-accelerating frame), no such outward force exists. What you feel when a car turns sharply is your body’s inertia trying to keep you moving in a straight line while the car provides a centripetal force to pull you into the turn. The sensation of being ‘thrown outward’ is simply the effect of inertia, not a genuine force pushing you outward.
OCR examiners frequently test this by asking students to identify the forces on a turning object. Always describe forces that other objects exert on the body (tension, weight, normal contact, friction), and label the resultant of these as the centripetal force. Avoid ever marking ‘centrifugal force’ on a free-body diagram in an inertial frame.
In the conical pendulum, a small mass is swung in a horizontal circle at the end of a string. The string tension T has a vertical component that balances the weight mg, and a horizontal component that provides the centripetal force. By resolving forces, you can derive the relationship between the angle θ of the string to the vertical and the speed: tan θ = v² / (rg). The period of a conical pendulum is often expressed as T = 2π √(L cos θ / g).
圆锥摆中，一个小物体系在绳子末端在水平面内做圆周运动。绳的拉力 T 的竖直分量平衡重力 mg，水平分量则提供向心力。通过力的分解，可以导出绳与竖直方向的夹角 θ 和速度的关系：tan θ = v² / (rg)。圆锥摆的周期常表达为 T = 2π √(L cos θ / g)。
For a banked track or road, the design is such that even without friction a vehicle can negotiate a curve at a specific speed. Resolving the normal reaction N vertically and horizontally gives: N cos θ = mg and N sin θ = mv² / r. Dividing yields tan θ = v² / (rg), which gives the ‘design speed’ v = √(rg tan θ). When friction is present, it acts along the slope to alter the safe speed range.
对于倾斜弯道（如赛车场弯道或铁路弯轨），其设计理念是使赛车在无摩擦力的情况下也能以特定速度安全过弯。将支持力 N 沿竖直和水平方向分解可得：N cos θ = mg，N sin θ = mv² / r。两式相除得到 tan θ = v² / (rg)，由此得出设计速度 v = √(rg tan θ)。当存在摩擦力时，摩擦力沿斜面方向影响安全速度的范围。
8. Vertical Circular Motion: Speed Variation and Tension | 竖直面圆周运动：速度变化与张力
Unlike horizontal circles, speed is not constant in vertical circular motion because gravity does work on the object as it rises and falls. The centripetal force requirement must still be met at every point, meaning the tension (or normal reaction) varies. At the bottom of the circle, the centripetal force is T – mg = mv² / r, so tension is largest. At the top, T + mg = mv² / r, giving the smallest tension. For a mass on a string, there is a critical minimum speed at the top: when T = 0, mg = mv² / r, so v_min = √(gr).
与水平面圆周运动不同，竖直面内做圆周运动的物体速率并不恒定，因为重力在物体上升和下降时做功。然而，每一点都必须满足向心力的需求，这意味着绳的张力（或支持力）在不断变化。在圆的最低点，向心力由 T – mg = mv² / r 提供，张力最大；在最高点，T + mg = mv² / r，张力最小。对于绳拴小球的情况，在最高点存在一个临界最小速度：当 T = 0 时，重力完全提供向心力，mg = mv² / r，因此 v_min = √(gr)。
For a rigid support (e.g., a car on a loop-the-loop track), the normal reaction can drop to zero but cannot pull; the minimum speed at the top remains v = √(gr). If the speed is lower than this, the object loses contact and falls off the track. In questions involving vertical circles, always identify the forces acting towards the centre at the point of interest and apply F_net = mv² / r.
对于刚性支撑（例如过山车在环形轨道上），支持力可以降至零但不能提供拉力；最高点处的最小速度仍为 v = √(gr)。若速度低于该值，物体将脱离轨道坠落。在涉及竖直圆周运动的题目中，应在所研究的点上找出指向圆心的所有力，并应用 F_net = mv² / r 求解。
9. Energy Considerations in Vertical Circles | 竖直圆周运动中的能量分析
Because the only dissipative force is usually negligible, mechanical energy is conserved in a vertical circle. You can relate the speed at any point to the height change from a reference level: ½ m v² + mgh = constant. This is especially handy when you know the speed at one position (say the bottom) and need the speed at another (such as the top). For a complete loop starting from the bottom with speed u, to just reach the top with speed √(gr), energy conservation gives: ½ m u² = ½ m (gr) + mg(2r), leading to the well-known condition u = √(5gr).
由于耗散力通常可忽略，竖直平面内的圆周运动满足机械能守恒。任意一点的速度均可通过相对参考点的高度差相关联：½ m v² + mgh = 常数。当已知某一点的速度（例如最低点）时，这一点特别便于求解另一点（如最高点）的速度。欲使小球从最低点出发完成一个完整圆环，最低点速度 u 需满足到达最高点时的速度至少为 √(gr)，利用能量守恒：½ m u² = ½ m (gr) + mg(2r)，由此导出经典条件 u = √(5gr)。
Energy arguments also appear when friction is present. In such cases, the work done against friction reduces the total mechanical energy. OCR exam questions may ask you to compare an ideal frictionless case with a real case, or to find the energy lost given the speed change over a segment of the circle.
10. Experimental Determination of Centripetal Force | 实验测定向心力
A classic OCR practical involves whirling a rubber bung tied to a string that passes through a glass tube, with a mass hanger attached to the lower end. By maintaining a constant radius (marked by a reference point) and measuring the period for a fixed number of revolutions, students calculate the centripetal force using F = m ω² r = m (2π / T)² r. This is then compared with the weight of the hanging mass, which equals the string tension at the top of the tube. The experiment verifies that the centripetal force equals the tension within experimental uncertainty.
OCR 经典实验之一是旋转一个系在绳子上的橡胶塞，绳子穿过一根玻璃管，下端悬挂一个质量钩码。通过保持旋转半径不变（可用标记点控制），并测量一定圈数对应的周期，学生可以利用 F = m ω² r = m (2π / T)² r 计算向心力。将此值与悬挂质量的重力（等于管顶处绳子的张力）进行比较，可在实验误差范围内验证向心力等于绳的张力。
Key sources of uncertainty include human reaction time in timing the revolutions, difficulty in keeping the radius truly constant, and friction between the string and the glass tube. Reducing uncertainty requires using more revolutions (say 50) to measure the total time, using low-friction tubes and ensuring the bung spins in a horizontal circle. OCR may ask you to suggest improvements or to sketch a graph of F against ω² to demonstrate the linear relationship.
主要误差来源包括人工计时的反应时间、难以保持严格的恒定半径以及绳子与玻璃管间的摩擦。减小误差的方法包括：计取较多圈数（如50圈）的总时间、使用低摩擦的管口、确保橡胶塞是在水平面内旋转。OCR 可能会要求你对实验提出改进建议，或绘制 F 与 ω² 的关系图来展示其线性关系。
11. Key Equations Summary and Exam Tips | 公式总结与应试技巧
Keeping all the principal formulas organised is half the battle. The table below collects every equation you need for A-Level OCR circular motion. For many problems, you will only need to identify the given quantities, convert to SI units (radians, seconds, metres) and pick the appropriate form of the centripetal force or acceleration equation.
θ measured from horizontal or vertical appropriately
Vertical circle (top, string)
v_min = √(gr)
T = 0 at top
Minimum speed for loop from bottom
u = √(5gr)
Energy conserved
Exam tip: always draw a clear free-body diagram showing forces acting on the object at the instant of interest. Resolve forces towards the centre, set the resultant equal to mv² / r, and solve. If the motion is non-uniform, supplement with energy conservation. Check that your answers are dimensionally consistent and that you have used radians for angular quantities where the radian is the natural unit.
应试技巧：一定要画出物体在所研究瞬间的清晰受力分析图。将力沿径向分解，令指向圆心的合力等于 mv² / r 并求解。如果运动是非匀速的，请结合能量守恒。检查答案量纲是否合理，并确保在采用弧度作为自然单位的场合下，角量确实使用了弧度。
Published by TutorHao | Physics Revision Series | aleveler.com
Capacitance is a core concept in both IB Physics (Topic 11.3) and OCR A Level Physics (Module 6.1). A thorough understanding of capacitors, their behaviour in circuits, energy storage, and the mathematics of RC charge/discharge is essential for high marks. This article covers all key points, linking theory to typical exam questions to help you master capacitance.
Capacitance (C) is defined as the charge stored per unit potential difference across a capacitor. It is a measure of a capacitor’s ability to store charge.
电容（C）定义为电容器每单位电势差所储存的电荷量。它衡量了电容器储存电荷的能力。
C = Q / V
The unit of capacitance is the farad (F), where 1 F = 1 C V⁻¹. In practice, capacitors often have values in microfarads (µF), nanofarads (nF) or picofarads (pF).
电容的单位是法拉（F），1 F = 1 C V⁻¹。实际应用中，电容器的数值常用微法（µF）、纳法（nF）或皮法（pF）表示。
2. Capacitance of a Parallel-Plate Capacitor | 平行板电容器的电容
For a parallel-plate capacitor, the capacitance is proportional to the plate area (A) and inversely proportional to the plate separation (d). The permittivity of free space (ε₀) is the constant of proportionality for a vacuum.
Where ε₀ ≈ 8.85 × 10⁻¹² F m⁻¹. If a dielectric material is inserted, the capacitance increases by a factor εᵣ (relative permittivity).
其中 ε₀ ≈ 8.85 × 10⁻¹² F m⁻¹。如果插入电介质材料，电容会增大 εᵣ（相对介电常数）倍。
3. Dielectrics and Relative Permittivity | 电介质与相对介电常数
A dielectric is an insulating material that becomes polarised in an electric field, reducing the effective field strength and allowing more charge to be stored for the same p.d. The relative permittivity (εᵣ), also called dielectric constant, is the ratio of the capacitance with the dielectric to the capacitance in a vacuum.
Exam questions often ask you to explain the effect of inserting a dielectric on capacitance, charge, potential difference, and energy stored. Remember that if the capacitor is connected to a battery, V remains constant; if isolated, Q remains constant.
A charged capacitor stores electrical potential energy. The energy stored can be derived from the work done to move charge against the potential difference, and it is given by the three equivalent expressions.
充电的电容器储存电势能。储存的能量可由反抗电势差移动电荷所做的功推导得出，共有三种等价表达式。
E = ½ QV = ½ CV² = ½ Q² / C
In exam problems, choose the most convenient formula based on the given quantities. The area under a Q–V graph represents the energy stored, which is important for multiple-choice and data-analysis questions.
When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances. This is because each capacitor experiences the same p.d. and total charge is the sum of charges.
电容器并联时，总电容等于各电容之和。这是因为每个电容器承受相同电势差，总电荷为各电荷之和。
C_total = C₁ + C₂ + C₃ + …
For series combinations, the reciprocal of the total capacitance is the sum of the reciprocals of the individual capacitances. All capacitors in series store the same charge, and the p.d. across each is inversely proportional to its capacitance.
Common exam traps involve mixing series and parallel circuits or applying these rules to energy and charge calculations. Always identify the configuration first.
常见考题陷阱包括混合串并联电路，或将这些规则应用于能量和电荷计算。务必先识别连接方式。
6. RC Circuits: Charging a Capacitor | RC 电路：电容器充电
When a capacitor is charged through a resistor from a steady p.d. source (V₀), the charge, voltage across the capacitor, and current follow exponential functions. The capacitor voltage grows as it approaches the supply voltage asymptotically.
The current decreases from its initial maximum (I₀ = V₀/R) according to I = I₀ e^(-t/RC). Similarly, the charge follows q = Q₀ (1 − e^(-t/RC)) where Q₀ = CV₀.
7. RC Circuits: Discharging a Capacitor | RC 电路：电容器放电
When a charged capacitor discharges through a resistor, the charge, voltage, and current all decay exponentially from their initial values (Q₀, V₀, I₀).
当充电的电容器通过电阻放电时，电荷、电压和电流均从其初始值（Q₀, V₀, I₀）开始指数衰减。
q = Q₀ e^(-t/RC)
V = V₀ e^(-t/RC)
The discharge current flows in the opposite direction to the charging current, and its magnitude decreases as |I| = I₀ e^(-t/RC).
放电电流方向与充电电流相反，其大小按 |I| = I₀ e^(-t/RC) 减小。
8. Time Constant and Graphical Analysis | 时间常数与图像分析
The time constant τ (tau) is defined as τ = RC. It has the unit of seconds. After a time equal to τ, the charge on a discharging capacitor falls to about 37% of its initial value; during charging, the charge reaches about 63% of its final value.
Graphs of Q, V, or I against time show exponential decay or growth. You must be able to determine τ from a graph by finding the time for the quantity to fall to 37% of its initial value, or by using the initial gradient method. In log-linear plots, the gradient equals –1/τ for discharge.
Q、V 或 I 随时间变化的图像呈现指数衰减或增长。你必须能从图像中求出 τ：找到电量降至初始值 37% 所需的时间，或使用初始切线法。在对数-线性图中，放电曲线的梯度等于 –1/τ。
9. Exponential Decay and Half-Life | 指数衰减与半衰期
For an RC discharging circuit, the half-life t₁/₂ is the time taken for the charge, voltage, or current to reduce by half. It is related to the time constant by t₁/₂ = τ ln 2 ≈ 0.693 RC. This relationship is analogous to radioactive decay and is a favourite topic for linking physics concepts.
Exam questions may ask you to calculate R or C from half-life measurements, or to sketch graphs showing the effect of doubling R or C on the discharge curve.
考题可能要求你根据半衰期测量值计算 R 或 C，或者画出 R 或 C 加倍后对放电曲线影响的示意图。
10. Practical Applications and Exam Tips | 实际应用与考试技巧
Capacitors are used in smoothing circuits for rectified power supplies, in timing circuits, camera flashes, and touch screens. Understanding the energy discharge rate helps explain why a flash can deliver a brief, intense burst of light.
In both IB and OCR exams, common mistakes include confusing series and parallel rules, misusing average power, or misinterpreting V–t graphs. Always check whether the capacitor is charging or discharging, and note if the circuit includes multiple resistors that affect τ.
For data-analysis questions, practice finding τ from graphs, applying C = ε₀εᵣA/d to real electrode dimensions, and rearranging logarithmic forms of exponential equations, such as ln(V) = ln(V₀) – t/RC.
对于数据分析题，要练习从图像求 τ、对实际电极尺寸应用 C = ε₀εᵣA/d，以及将指数方程转换为对数形式，如 ln(V) = ln(V₀) – t/RC。
Published by TutorHao | Physics Revision Series | aleveler.com
Dynamics is the branch of physics that deals with the motion of objects and the forces causing this motion. In the IGCSE WJEC Physics specification, dynamics covers essential concepts such as Newton’s laws of motion, momentum, impulse, and the conservation of momentum. Understanding these principles is crucial for explaining everyday phenomena like car crashes, sports, and rocket launches. This revision guide breaks down the key points you need to master for the exam.
1. Newton’s First Law of Motion (Law of Inertia) | 牛顿第一定律（惯性定律）
Newton’s first law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by a resultant external force.
牛顿第一定律指出，除非受到合外力的作用，否则物体将保持静止或匀速直线运动状态。
This property of an object to resist changes in its state of motion is called inertia. The greater the mass of an object, the greater its inertia.
物体抵抗其运动状态变化的这种性质称为惯性。物体的质量越大，其惯性就越大。
For example, a passenger lurches forward when a bus brakes suddenly because their body tends to continue moving at the original velocity due to inertia.
例如，当公交车突然刹车时，乘客会向前倾，因为他们的身体由于惯性倾向于保持原来的速度运动。
In space, where there is almost no external force, a spacecraft will continue moving at constant velocity without using its engines, demonstrating the law.
在几乎没有外力的太空中，航天器无需发动机就能继续以恒定速度运动，这证明了该定律。
2. Newton’s Second Law (F = ma) | 牛顿第二定律（F = ma）
Newton’s second law relates the resultant force acting on an object to its acceleration:
F = m a
牛顿第二定律将作用在物体上的合力与其加速度联系起来：
F = m a
Here, F is the resultant force in newtons (N), m is the mass in kilograms (kg), and a is the acceleration in metres per second squared (m/s²). The acceleration is directly proportional to the force and inversely proportional to the mass.
These two forces are of the same type, act on different bodies, and have the same magnitude but opposite direction. They are often called action and reaction forces.
这两个力是同种性质的力，作用在不同的物体上，大小相等但方向相反。它们通常被称为作用力和反作用力。
For example, when you push against a wall, the wall pushes back on you with an equal force. The force you apply does not cancel the reaction because they act on different objects.
4. Mass, Weight, and Gravitational Field Strength | 质量、重量与引力场强度
Mass is the amount of matter in an object and is measured in kilograms (kg). It is a scalar quantity and remains the same everywhere in the universe.
质量是物体所含物质的多少，以千克（kg）为单位。它是标量，在宇宙中任何地方都保持不变。
Weight is the gravitational force acting on an object and is measured in newtons (N). It depends on the gravitational field strength (g) and mass (m):
W = m g
重量是作用在物体上的重力，以牛顿（N）为单位。它取决于引力场强度（g）和质量（m）：
W = m g
Gravitational field strength g on Earth is about 9.8 N/kg. On the Moon, g ≈ 1.6 N/kg, so your weight would be much less, but your mass unchanged.
地球上的引力场强度 g 约为 9.8 N/kg。月球上 g ≈ 1.6 N/kg，因此你的体重会轻很多，但质量不变。
The table below summarises the key differences between mass and weight:
下表总结了质量和重量的主要区别：
Property
Mass
Weight
Definition
Amount of matter
Gravitational pull
Unit
kg
N
Depends on
Quantity of matter
Mass and g
Measured with
Balance
Spring scale / newton meter
Mass is measured using a balance, whereas weight is measured using a spring scale or newton meter.
质量使用天平测量，而重量使用弹簧秤或牛顿计测量。
5. Resultant Force and Free-Body Diagrams | 合力和受力图
The resultant (net) force is the vector sum of all forces acting on an object. When forces are balanced, the resultant force is zero, and the object moves with constant velocity or stays at rest.
合力是作用在物体上所有力的矢量和。当力平衡时，合力为零，物体保持匀速运动或静止状态。
Free-body diagrams are simplified sketches showing all forces acting on a single object, using arrows to indicate magnitude and direction.
受力图是显示作用在单个物体上所有力的简图，用箭头表示力的大小和方向。
For an object on a horizontal surface, typical forces include weight (downwards), normal reaction (upwards), applied force, and friction.
对于水平面上的物体，常见的力有重力（向下）、法向反作用力（向上）、施加的力和摩擦力。
When drawing free-body diagrams, arrows must be drawn to scale and labeled correctly. The resultant force can be found by vector addition.
画受力图时，箭头必须按比例绘制并正确标注。合力可以通过矢量加法求得。
6. Momentum and Impulse | 动量和冲量
Momentum p is the product of mass and velocity:
p = m v
动量 p 是质量与速度的乘积：
p = m v
It is a vector quantity measured in kg m/s.
动量是矢量，单位为 kg m/s。
Impulse is the product of force and the time for which it acts, and it equals the change in momentum:
F Δt = Δp = m v – m u
冲量是力与其作用时间的乘积，等于动量的变化量：
F Δt = Δp = m v – m u
where u is initial velocity and v is final velocity.
其中 u 是初速度，v 是末速度。
The impulse-momentum relationship explains why airbags are used in cars: they increase the time over which the force acts during a collision, reducing the force experienced by passengers.
冲量-动量关系解释了为什么汽车使用安全气囊：它们延长了碰撞时力作用的时间，从而减小了乘客受到的力。
In sports, the follow-through in hitting a ball increases contact time, leading to a greater change in momentum and thus a faster ball speed.
在体育运动中，击球后的顺势动作增加了接触时间，导致更大的动量变化，从而球速更快。
7. Conservation of Momentum | 动量守恒
The law of conservation of momentum states that in a closed system (no external forces), the total momentum before a collision or explosion equals the total momentum after.
动量守恒定律指出，在封闭系统中（无外力），碰撞或爆炸前的总动量等于碰撞或爆炸后的总动量。
For a collision between two objects A and B:
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
对于两个物体A和B之间的碰撞：
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
In an explosion, the total momentum is zero before and after, so the two fragments move in opposite directions with equal and opposite momenta.
在爆炸中，前后总动量为零，因此两个碎片以大小相等、方向相反的动量反向运动。
Problems often involve calculating velocities after a collision or recoil speed in gun-shooting scenarios.
问题通常涉及计算碰撞后的速度或枪击情形中的反冲速度。
Inelastic collisions are those where kinetic energy is not conserved (though momentum is). Perfectly inelastic collisions result in objects sticking together.
非弹性碰撞是指动能不守恒（但动量守恒）的碰撞。完全非弹性碰撞导致物体粘在一起。
8. Terminal Velocity and Air Resistance | 终端速度与空气阻力
When an object falls through a fluid (liquid or gas), it experiences air resistance (drag) that increases with speed.
当物体在流体（液体或气体）中下落时，会受到随速度增加而增大的空气阻力（阻力）。
Initially, the weight is greater than the drag, resulting in a downward acceleration. As speed increases, drag grows until it equals the weight.
初始时，重量
Published by TutorHao | IGCSE Physics Revision Series | aleveler.com
📚 Deriving Key Formulas from the A-Level Physics Data and Formula Booklet (January 2018) | A-Level物理数据与公式小册子（2018年1月）关键公式推导
Understanding where formulas come from deepens your grasp of physics and helps you apply them correctly. This article walks you through derivations of key equations found in the A-Level Physics Data and Formula Booklet (January 2018 edition), covering mechanics, waves, electricity, thermal physics and more.
The SUVAT equations relate displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t) for uniform acceleration. They are derived directly from the definitions of velocity and acceleration.