📚 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.
IB 物理要求学生在多个主题中吸收大量概念、公式和实验技巧。思维导图将这份密集的课程转化为视觉化、相互关联的知识网络，在考试中更容易记忆和提取。通过围绕核心主题组织知识，并用简洁的提示向外分支，你能够快速回忆起整个专题的要点。
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.
把核心科目“IB 物理”放在页面中央。从中心辐射出八条主要分支，对应标准课程的各个主题。为每个分支使用不同颜色，为关键物理量绘制简单图标（例如，用弹簧表示力，用电池表示电学），每个节点限制在一到两个关键词。这样就能在一张图中形成整体概览，激发你长期记忆中储存的详细知识。
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.
复习时，遮住思维导图的部分内容，自测其中的关联与公式。久而久之，你的大脑会将视觉布局与背后的物理原理联系起来，从而在考场中闪电般提取信息。
2. Measurements and Uncertainties | 测量与不确定性
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.
从“测量与不确定性”分支开始，写出基本国际单位的子节点。七个基本单位是千克（kg）、米（m）、秒（s）、安培（A）、摩尔（mol）、开尔文（K）和坎德拉（cd）。物理学中所有其他单位都源于这七个。
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%.
添加关于不确定度和有效数字的子分支。对于数字式仪器，绝对不确定度为最小刻度值的一半；对于模拟式仪器，则为最小刻度值。相对不确定度是绝对不确定度除以测量值，百分比不确定度则再乘以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)
Fractional uncertainty = Δx / x ; Percentage uncertainty = (Δx / x) × 100%
矢量分量：Fₓ = F cosθ , Fᵧ = F sinθ
3. Mechanics | 力学
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.
画出“力学”主分支，并分出运动学、力、功、能量与功率，以及动量与冲量。对于运动学，核心是“SUVAT”方程，将它们与匀加速直线运动的条件关联起来。
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.
动量分支将冲量与动量变化联系起来：F Δt = Δp = m(v – u)。动量守恒定律对于碰撞和爆炸问题至关重要，尤其是二维情况。
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.
热学分支围绕温度、热传递和气体定律展开。用粒子平均随机动能来定义温度。在思维导图中清晰区分热能与温度。
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.
分支到电路图：串联电阻相加（R_total = R₁ + R₂ + …），并联电阻遵循 1/R_total = 1/R₁ + 1/R₂ + …。基尔霍夫电流定律（节点定则）和电压定律（回路定则）支配着复杂电路。
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.
向心力是产生这一加速度的合力，它不是一个独立的力，而是已有力（张力、摩擦力、重力）的合力。对于转弯的汽车，摩擦力提供向心力。
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.
放射性衰变由指数定律 N = N₀ e^(–λ t) 描述，半衰期 t½ = ln 2 / λ。熟记辐射类型——α（⁴₂He）、β（e⁻ 或 e⁺）和γ（电磁波）——及其穿透能力。
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).
“能源生产”分支将物理概念与现实电源连接起来。在化石燃料下，注意能量密度和二氧化碳的产生。记住桑基图可以直观显示能量转化与效率：效率 = （有用功率输出）/（总功率输入）。
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.
太阳能、风能和水电等可再生能源各有优缺点。光伏电池直接将太阳能转化为电能，而风力发电机转化空气的动能。在所有能量链中，应描述一次能源和基于电磁感应原理的发电机。
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。
s = λ D / d ; ΔΦ = N B A cosθ ; ε = – ΔΦ / Δt
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