📚 IB and AQA Physics: End-of-Term Revision Guide | IB 与 AQA 物理：期末复习提纲
As the end of term approaches, students following either the IB Diploma Physics course or the AQA A-level Physics specification need a focused revision strategy. This guide consolidates the core topics common to both syllabi, highlighting essential concepts, key equations, and typical exam pitfalls.
随着期末临近，无论是学习 IB 文凭物理还是 AQA A-level 物理的学生都需要有针对性的复习策略。本提纲整合了两份大纲共有的核心主题，突出基本概念、关键方程和常见考试陷阱。
1. Measurements and Uncertainties | 测量与不确定性
Understand the difference between random and systematic errors, and be able to express uncertainties in measurements using absolute, fractional and percentage forms.
理解随机误差与系统误差的区别，并能够用绝对误差、相对误差和百分数形式表示测量中的不确定度。
When combining uncertainties, remember: for addition and subtraction, add absolute uncertainties; for multiplication and division, add percentage uncertainties.
当合成不确定度时记住：加减运算，将绝对不确定度相加；乘除运算，则将百分数不确定度相加。
Plot graphs using error bars and be ready to determine gradients and intercepts, including the uncertainties in these values based on lines of best fit and worst fit.
使用误差棒绘制图表，并会确定斜率和截距，包括根据最佳拟合线和最差拟合线求这些值的不确定度。
| Operation (English) | 运算 (中文) | Uncertainty Combination |
| Addition/Subtraction | 加 / 减 | Add absolute uncertainties (ΔA + ΔB) |
| Multiplication/Division | 乘 / 除 | Add percentage uncertainties (%εA + %εB) |
If y = a ± b, then Δy = Δa + Δb
If y = a × b or y = a / b, then %εy = %εa + %εb
2. Mechanics: Kinematics | 力学：运动学
Define displacement, velocity, acceleration and distinguish vector from scalar quantities. Recognise the conditions under which the suvat equations can be applied.
定义位移、速度、加速度，并区分矢量和标量。认出在何种条件下可以应用 suvat 方程。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
Interpret displacement-time, velocity-time and acceleration-time graphs, paying special attention to gradients representing velocity and acceleration, and areas under curves representing displacement and change in velocity.
解释位移-时间图、速度-时间图和加速度-时间图，特别注意斜率表示速度和加速度，曲线下的面积表示位移和速度变化。
For projectile motion, treat horizontal and vertical components independently. The horizontal velocity remains constant, while the vertical motion is governed by uniform acceleration due to gravity, g = 9.81 m s⁻².
对于抛体运动，独立处理水平分量和竖直分量。水平速度保持不变，而竖直运动则由重力加速度 g = 9.81 m s⁻² 决定。
3. Mechanics: Forces and Newton’s Laws | 力学：力与牛顿定律
Start with free-body diagrams showing all forces acting on an object. Newton’s first law: an object remains at rest or in uniform motion unless a resultant force acts. Second law: F = ma. Third law: every action has an equal and opposite reaction.
从显示物体上所有作用力的自由体图开始。牛顿第一定律：物体保持静止或匀速直线运动，除非有合力作用。第二定律：F = ma。第三定律：每一个作用力都有一个等大反向的反作用力。
Be confident resolving forces into perpendicular components. Use F = ma in both linear and equilibrium situations, where resultant force is zero.
熟练地将力分解为相互垂直的分量。在线性运动和合力为零的平衡状态中都能运用 F = ma。
Friction: distinguish static from dynamic friction. The maximum static friction is fₛ(max) = μₛR, while dynamic friction is fₖ = μₖR. Always draw friction opposite to motion or potential motion.
摩擦力：区分静摩擦和动摩擦。最大静摩擦力 fₛ(max) = μₛR，动摩擦力 fₖ = μₖR。总是把摩擦力画在与运动或潜在运动相反的方向上。
4. Work, Energy and Power | 功、能量与功率
Work done is W = Fs cosθ, where θ is the angle between force and displacement. Energy is the capacity to do work. Understand energy transfers in systems and the principle of conservation of energy.
功 W = Fs cosθ，其中 θ 是力与位移的夹角。能量是做功的本领。理解系统内的能量转移和能量守恒原理。
Kinetic energy: Eₖ = ½mv². Gravitational potential energy: Eₚ = mgΔh. Elastic potential energy: Eₑ = ½kx² (for a spring obeying Hooke’s law).
动能：Eₖ = ½mv²。重力势能：Eₚ = mgΔh。弹性势能：Eₑ = ½kx²（遵守胡克定律的弹簧）。
Power is rate of work done: P = W/t = Fv. Efficiency = useful power output / total power input. Always express efficiency as percentage or decimal.
功率是做功的快慢：P = W/t = Fv。效率 = 有用输出功率 / 总输入功率。始终用百分数或小数表达效率。
5. Thermal Physics | 热物理学
Define temperature in terms of average kinetic energy. Convert between Celsius and Kelvin: T(K) = T(°C) + 273.15. The specific heat capacity c relates energy change to temperature change: Q = mcΔθ.
用平均动能定义温度。在摄氏度和开尔文之间转换：T(K) = T(°C) + 273.15。比热容 c 将能量变化与温度变化联系起来：Q = mcΔθ。
During phase changes, latent heat L is involved: Q = mL, with temperature remaining constant. Distinguish specific latent heat of fusion and vaporisation.
在相变过程中，涉及潜热 L：Q = mL，温度保持恒定。区分熔化比潜热和汽化比潜热。
For an ideal gas: pV = nRT, where n is number of moles and R = 8.31 J mol⁻¹ K⁻¹. Also the combined gas law: p₁V₁/T₁ = p₂V₂/T₂ for a fixed mass.
对于理想气体：pV = nRT，其中 n 是摩尔数，R = 8.31 J mol⁻¹ K⁻¹。还有固定质量下的联合气体定律：p₁V₁/T₁ = p₂V₂/T₂。
Understand Brownian motion as evidence of molecular motion and the kinetic model linking pressure to particle collisions.
理解布朗运动是分子运动的证据，以及将压强与粒子碰撞联系起来的动力学模型。
6. Waves | 波
Wave properties: amplitude A, wavelength λ, frequency f, period T, and wave speed v = fλ. Differentiate transverse and longitudinal waves with examples (e.g. light vs sound).
波的性质：振幅 A、波长 λ、频率 f、周期 T，以及波速 v = fλ。区分横波和纵波并举例（例如光与声）。
Principle of superposition leads to constructive and destructive interference. For two coherent sources, path difference determines the interference pattern. Young’s double-slit: Δy = λD/d.
叠加原理导致相长干涉和相消干涉。对于两个相干源，程差决定干涉图样。杨氏双缝：Δy = λD/d。
Standing waves form on strings and in pipes. For a string fixed at both ends, λ = 2L/n with harmonics n = 1,2,3… For an open pipe, the same pattern; closed pipe has only odd harmonics.
驻波在弦上和管中形成。对于两端固定的弦，λ = 2L/n，谐波 n = 1,2,3… 开管遵循相同模式；闭管仅有奇数谐波。
Doppler effect: observed frequency changes when source and observer move relative to each other. f ‘ = f (v ± vₒ)/(v ± vₛ). Use the signs carefully.
多普勒效应：当波源和观察者相对运动时，观测到的频率发生变化。f ‘ = f (v ± vₒ)/(v ± vₛ)。仔细选用符号。
7. Electricity and Circuits | 电学与电路
Ohm’s law: V = IR for ohmic conductors at constant temperature. Resistance R = ρL/A. Conductivity is the reciprocal of resistivity.
欧姆定律：在恒温下对于欧姆导体有 V = IR。电阻 R = ρL/A。电导率是电阻率的倒数。
Kirchhoff’s first law (junction rule): sum of currents entering a junction equals sum leaving. Second law (loop rule): sum of emfs around any closed loop equals sum of potential drops.
基尔霍夫第一定律（节点定律）：流入节点的电流之和等于流出电流之和。第二定律（回路定律）：任意闭合回路中电动势的代数和等于电位降的代数和。
Internal resistance r of a cell: terminal p.d. V = ε – Ir. The emf ε can be found from the intercept of a V-I graph.
电池的内阻 r：端电压 V = ε – Ir。电动势 ε 可以从 V-I 图的截距求得。
Power in circuits: P = IV = I²R = V²/R. Understand energy dissipation in resistors and transfer in components.
电路中的功率：P = IV = I²R = V²/R。理解电阻器中的能量耗散和元器件中的能量转移。
8. Circular Motion and Gravitation | 圆周运动与万有引力
For an object moving at constant speed in a circle, the velocity direction changes continuously. Centripetal acceleration a = v²/r = ω²r, and centripetal force F = mv²/r = mω²r, directed towards the centre.
对于以恒定速率做圆周运动的物体，速度方向持续变化。向心加速度 a = v²/r = ω²r，向心力 F = mv²/r = mω²r，指向圆心。
Newton’s law of gravitation: F = Gm₁m₂/r². Gravitational field strength g = GM/r². For a planet, g is approximately constant near the surface.
牛顿万有引力定律：F = Gm₁m₂/r²。引力场强度 g = GM/r²。对于行星，表面附近的 g 近似为常量。
Kepler’s third law: T² ∝ r³ for planets orbiting the same star. Derive it by equating centripetal force to gravitational force.
开普勒第三定律：围绕同一星体的行星，T² ∝ r³。可通过令向心力等于万有引力来推导。
9. Atomic, Nuclear and Particle Physics | 原子、核与粒子物理
Atomic structure: nucleus containing protons and neutrons, surrounded by electrons in discrete energy levels. Transitions between levels explain emission and absorption spectra.
原子结构：包含质子和中子的原子核，被处于分立能级的电子环绕。能级跃迁解释了发射光谱和吸收光谱。
Radioactive decay: activity A = λN, and the exponential decay law N = N₀e⁻λᵗ. Half-life t₁/₂ = ln2/λ. Distinguish alpha, beta-minus, beta-plus, gamma decays.
放射性衰变：活度 A = λN，指数衰变律 N = N₀e⁻λᵗ。半衰期 t₁/₂ = ln2/λ。区分 α 衰变、β⁻ 衰变、β⁺ 衰变和 γ 衰变。
In particle physics, quarks and leptons are fundamental. Protons are uud, neutrons are udd. Conservation laws for charge, baryon number, lepton number apply in all interactions.
在粒子物理中，夸克和轻子是基本的。质子是 uud，中子是 udd。在所有相互作用中，电荷、重子数、轻子数守恒定律成立。
Mass-energy equivalence: E = mc². In nuclear reactions, mass defect is converted to kinetic energy.
质能等价：E = mc²。在核反应中，质量亏损转化为动能。
10. Energy Production and Astrophysics | 能源生产与天体物理
Energy sources: fission, fusion, solar, wind, tidal, fossil fuels. Compare their power outputs, efficiency, and environmental impacts. Understand Sankey diagrams to represent energy transfers.
能源：裂变、聚变、太阳能、风能、潮汐能、化石燃料。比较它们的输出功率、效率和环境影响。理解桑基图来表示能量转移。
For IB/AQA astrophysics option: luminosity L = 4πd²b, where b is apparent brightness. Stefan-Boltzmann law: L = 4πR²σT⁴. Wien’s displacement law: λₘₐₓT = 2.9 × 10⁻³ m K.
对于 IB/AQA 天体物理选修部分：光度 L = 4πd²b，其中 b 是视亮度。斯特藩-玻尔兹曼定律：L = 4πR²σT⁴。维恩位移定律：λₘₐₓT = 2.9 × 10⁻³ m K。
The Hertzsprung-Russell diagram classifies stars by their luminosity and temperature, from main sequence to red giants and white dwarfs. Fusion processes vary with stellar mass.
赫罗图通过光度和温度对恒星分类，从主序星到红巨星和白矮星。聚变过程随恒星质量变化。
11. Practical Skills and Data Analysis | 实验技能与数据分析
Plan experiments to test relationships, identify independent, dependent and control variables. Ensure repeatable, reproducible and precise measurements.
设计实验来检验关系，识别自变量、因变量和控制变量。确保测量可重复、可复现且精确。
Analyse data using linear graphs; transform exponentially decaying data by taking natural logarithms to find constants. ln(N) against t yields a straight line with slope -λ.
利用线性图分析数据；通过取自然对数将指数衰减数据转化为直线。ln(N) 对 t 的图得到斜率为 -λ 的直线。
Evaluate uncertainties in final results, comment on percentage differences, and discuss systematic and random errors in conclusions. Always relate findings back to the original hypothesis.
评估最终结果的不确定度，评论百分差，并在结论中讨论系统误差和随机误差。始终将发现与原假设联系起来。
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