📚 Mind Map Quick Memorisation for IB & CIE Physics | IB CIE 物理：思维导图速记
Physics can feel like a mountain of disconnected formulas and definitions, but a mind map approach turns it into a web of logical connections. For IB and CIE candidates, building a single central image for each topic and branching out with key equations, graphs, and real-world links slashes revision time by more than half. This guide walks you through a complete mind-map framework, covering every major syllabus area, so you can memorise efficiently and recall effortlessly under exam pressure.
物理常常让人觉得是一堆互不相关的公式和定义，但用思维导图的方式能把它们变成一张逻辑连接网。对 IB 和 CIE 考生来说，为每个主题建立一张中心图，再分支列出关键方程、图像和现实联系，能将复习时间缩短一半以上。本文带你走完一套完整的思维导图框架，覆盖所有主要考纲领域，让你高效记忆，在考试压力下也能轻松提取。
1. Kinematics & Motion Graphs | 运动学与运动图像
The central node for this topic is simply ‘Motion’. One main branch carries the four SUVAT equations for constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u+v)t. Another branch handles motion graphs: for a displacement-time graph, the slope gives velocity; for a velocity-time graph, the slope gives acceleration and the area under the curve gives displacement. A third branch captures projectile motion as the combination of constant horizontal velocity and constant vertical acceleration g = 9.81 m s⁻².
这个主题的中心节点就是“运动”。一个主分支承载匀加速的四个 SUVAT 方程：v = u + at，s = ut + ½at²，v² = u² + 2as，以及 s = ½(u+v)t。另一个分支处理运动图像：对位移-时间图，斜率表示速度；对速度-时间图，斜率表示加速度，曲线下面积表示位移。第三个分支把握抛体运动，它是水平方向匀速与竖直方向恒定加速度 g = 9.81 m s⁻² 的合成。
s = ut + ½at²
2. Forces & Newton’s Laws | 力与牛顿定律
Draw ‘Force’ at the centre. From it branch Newton’s three laws: ‘Law of Inertia’ (constant velocity unless net force), ‘Fₙₑₜ = ma’, and ‘Action–Reaction pairs’. A separate branch collects the most common force rules: weight W = mg, tension T, normal reaction N, and friction f ≤ μN. For inclined planes, resolve mg into parallel (mg sin θ) and perpendicular (mg cos θ) components. The mind map should also link to free-body diagrams as a visual tool for setting up equations.
在中心写下“力”。由此分出牛顿三定律：’惯性定律’（无净外力则速度不变），“Fₙₑₜ = ma”，以及’作用力与反作用力对’。另一个分支汇集最常见的力：重力 W = mg，张力 T，法向反力 N，以及摩擦力 f ≤ μN。对于斜面，将 mg 分解为沿面的 mg sin θ 和垂直于面的 mg cos θ。思维导图还应把受力示意图作为一个视觉工具分支，用于列方程。
Fₙₑₜ = ma
3. Energy, Work & Power | 能量、功与功率
The hub is ‘Energy’. Two key branches split into kinetic energy Eₖ = ½mv² and gravitational potential energy Eₚ = mgh. The work–energy theorem bridges them: net work equals change in kinetic energy. Power P = ΔW/Δt and the alternative form P = Fv sit on a ‘Power’ branch. Another branch reminds you that energy is conserved but can become ‘dissipated’ as internal energy due to friction. For springs, add elastic potential energy Eₑ = ½kx².
中心是“能量”。两个关键分支分别为动能 Eₖ = ½mv² 和重力势能 Eₚ = mgh。功-能定理将二者连接：净功等于动能的变化。功率 P = ΔW/Δt 及其替代形式 P = Fv 放在“功率”分支上。另一个分支提醒你能量守恒，但可因摩擦’耗散’为内能。对弹簧，加上弹性势能 Eₑ = ½kx²。
4. Momentum & Impulse | 动量与冲量
Place ‘Momentum’ at the centre. The definition branch gives p = mv, a vector. The impulse branch connects impulse J = FΔt = Δp. The conservation branch is crucial: in collisions and explosions, total momentum before equals total momentum after, provided no external resultant force acts. Distinguish elastic collisions (kinetic energy conserved) from inelastic collisions (some KE converted). For IB HL and CIE A2, include the equation for relative speed in elastic collisions: v₂ − v₁ = −(u₂ − u₁).
中心放上“动量”。定义分支给出 p = mv，是矢量。冲量分支连接冲量 J = FΔt = Δp。守恒分支至关重要：在碰撞与爆炸中，只要无合外力作用，总动量前后相等。区分弹性碰撞（动能守恒）和非弹性碰撞（部分动能转化）。IB HL 和 CIE A2 还要包含弹性碰撞的相对速度式：v₂ − v₁ = −(u₂ − u₁)。
5. Circular Motion & Gravitation | 圆周运动与万有引力
The mind map starts with ‘Circular Motion’. Radial branch: centripetal acceleration a = v²/r = ω²r, centripetal force F = mv²/r = mω²r. The angular branch defines ω = 2π/T, v = ωr. For gravitation, the central force is Newton’s law: F = GMm/r². Combine it with centripetal force for satellites: GMm/r² = mv²/r, leading to orbital speed v = √(GM/r). Kepler’s third law T² ∝ r³ fits on the same branch. Gravitational field strength g = GM/r² can be mapped separately for point masses and inside a uniform sphere (only counts material inside radius r).
思维导图从“圆周运动”起始。径向分支：向心加速度 a = v²/r = ω²r，向心力 F = mv²/r = mω²r。角量分支定义 ω = 2π/T，v = ωr。转到万有引力，中心力是牛顿定律：F = GMm/r²。与向心力结合可得卫星运动：GMm/r² = mv²/r，导出轨道速度 v = √(GM/r)。开普勒第三定律 T² ∝ r³ 放在同一分支。引力场强度 g = GM/r² 可分别画出点质量与均匀球体内外的情况（球内只计半径 r 内的质量）。
6. Thermal Physics | 热物理
Use ‘Thermal’ as the centre. One main branch is temperature scales and the absolute zero (−273 °C). Another branch handles specific heat capacity Q = mcΔθ and specific latent heat Q = mL. The kinetic model branch links pressure, volume and temperature for an ideal gas: pV = nRT = NkₘT, with average kinetic energy per particle = (3/2)kₘT. A crucial sub-branch shows that p ∝ 1/V at constant T (Boyle), V ∝ T at constant p (Charles), and p ∝ T at constant V (Gay-Lussac). The first law of thermodynamics ΔU = Q − W sums up energy transfers.
以“热”为中心。一个主分支是温标和绝对零度（−273 °C）。另一个分支处理比热容 Q = mcΔθ 和比潜热 Q = mL。分子动力模型分支将理想气体的压强、体积与温度连接起来：pV = nRT = NkₘT，平均分子动能 = (3/2)kₘT。一个重要的子分支展示 T 不变时 p ∝ 1/V（玻意耳），p 不变时 V ∝ T（查理），V 不变时 p ∝ T（盖-吕萨克）。热力学第一定律 ΔU = Q − W 总结能量传递。
7. Waves & Oscillations | 波与振动
The core is ‘Waves’. Branch 1: wave types – transverse and longitudinal. Branch 2: wave equation v = fλ. Branch 3: intensity I ∝ amplitude², and for a spherical wave I ∝ 1/r². Branch 4 connects phase difference, path difference, and superposition: constructive interference when path difference = nλ, destructive when = (n+½)λ. For standing waves, nodes and antinodes appear at fixed positions. A separate ‘Simple Harmonic Motion’ branch gives a = −ω²x, with energy interchanging between kinetic and potential. Time period of mass-spring system T = 2π√(m/k) and pendulum T = 2π√(L/g) complete the map.
核心是“波”。分支一：波的类型——横波与纵波。分支二：波速方程 v = fλ。分支三：强度 I ∝ 振幅²，球面波 I ∝ 1/r²。分支四将相位差、波程差与叠加联系起来：波程差 = nλ 时相长干涉，= (n+½)λ 时相消干涉。对驻波，波节和波腹位于固定位置。一个独立的“简谐运动”分支给出 a = −ω²x，能量在动能与势能之间转换。弹簧振子周期 T = 2π√(m/k) 与单摆周期 T = 2π√(L/g) 完善该图谱。
8. Electricity & Direct Current Circuits | 电学与直流电路
At the centre write ‘Electricity’. Branch from it: ‘Charge & Current’ (I = ΔQ/Δt), ‘Potential Difference & EMF’ (V = W/Q), ‘Resistance & Ohm’s Law’ (V = IR). Resistor combinations form a sub-branch: series R = R₁ + R₂, parallel 1/R = 1/R₁ + 1/R₂. The power branch contains P = IV = I²R = V²/R. Circuit rules are vital: Kirchhoff’s current law (ΣI entering = ΣI leaving) and voltage law (ΣV in a loop = 0). Add internal resistance r: terminal p.d. = ε − Ir. Potential dividers and sensor circuits (LDR, thermistor) extend the diagram for practical applications.
中心写上“电学”。由此分支：“电荷与电流” (I = ΔQ/Δt)，“电势差与电动势” (V = W/Q)，“电阻与欧姆定律” (V = IR)。电阻组合形成一个子分支：串联 R = R₁ + R₂，并联 1/R = 1/R₁ + 1/R₂。电功率分支包含 P = IV = I²R = V²/R。电路规则至关重要：基尔霍夫电流定律（ΣI 进 = ΣI 出）和电压定律（回路 ΣV = 0）。加上内阻 r：端电压 = ε − Ir。电位分压器和传感器电路（LDR、热敏电阻）延展图示，用于实际应用。
9. Magnetism & Electromagnetic Induction | 磁学与电磁感应
The ‘Magnetism’ mind map starts with field lines: from N to S outside a magnet, and rules for current-carrying wires: right-hand grip rule gives circular fields around a straight wire, and a solenoid yields a uniform field like a bar magnet. Force on a current-carrying wire: F = BIL sin θ; on a moving charge: F = Bqv sin θ. For electromagnetic induction, Faraday’s law ε = −N ΔΦ/Δt is the trunk. Lenz’s law signs the direction: induced current opposes the flux change. The generator effect and transformer equation Vₚ/Vₛ = Nₚ/Nₛ sit on an ‘Applications’ branch.
“磁学”思维导图从磁感线开始：磁体外从 N 到 S，载流导线的右手螺旋定则给出直线周围的环形磁场，螺线管产生类似条形磁铁的匀强磁场。载流导线受力：F = BIL sin θ；运动电荷受力：F = Bqv sin θ。电磁感应方面，法拉第定律 ε = −N ΔΦ/Δt 是主干。楞次定律定方向：感应电流阻碍磁通量变化。发电机效应和变压器方程 Vₚ/Vₛ = Nₚ/Nₛ 放在“应用”分支。
10. Atomic, Nuclear & Particle Physics | 原子、核与粒子物理
‘Atom’ sits at the centre. Branches include: Rutherford’s scattering experiment → nuclear atom; electrons in discrete energy levels; emission and absorption spectra. Nuclear structure links A, Z, N with isotope notation. Radioactive decay: activity A = λN, decay law N = N₀e⁻
“原子”居于中心。分支包括：卢瑟福散射实验 → 核式原子；电子处在分立能级；发射与吸收光谱。核结构将 A、Z、N 与同位素符号联系起来。放射性衰变：活度 A = λN，衰变律 N = N₀e⁻
| Radiation | Nature | Penetration | Ionisation |
| α | Helium nucleus | Low | High |
| β⁻ | Fast electron | Medium | Medium |
| γ | EM radiation | High | Low |
11. Quantum & Nuclear Physics (HL) | 量子与核物理提高
For Higher Level and A2 depth, ‘Quantum’ becomes its own centre. The photoelectric effect branch contains E = hf, the work function Φ, and Einstein’s equation hf = Φ + Eₖ max. The wave–particle duality branch includes de Broglie wavelength λ = h/p. Electron diffraction evidence and the uncertainty principle ΔxΔp ≥ h/4π tie the picture together. In nuclear physics, mass defect and binding energy E = Δmc² must be calculated with unified atomic mass unit conversions. The Bohr model for hydrogen and energy level calculations using Eₙ = −13.6/n² eV form a separate ‘Atomic Spectra’ branch.
对 HL 和 A2 深度内容，“量子”自成中心。光电效应分支包含 E = hf，功函数 Φ，以及爱因斯坦方程 hf = Φ + Eₖ max。波粒二象性分支包括德布罗意波长 λ = h/p。电子衍射证据和不确定原理 ΔxΔp ≥ h/4π 将图景联系起来。在核物理中，要通过统一原子质量单位换算计算质量亏损和结合能 E = Δmc²。玻尔氢原子模型和能级计算 Eₙ = −13.6/n² eV 形成一个独立的“原子光谱”分支。
12. Practical Skills & Data Analysis | 实验技能与数据分析
The final mind map doesn’t focus on theory but on ‘Experiments’ and ‘Data’. Branches cover: measurement uncertainties (absolute, fractional, percentage); combining uncertainties for sums/differences (add absolute) and products/quotients (add percentage); systematic vs. random errors. Graph skills branch: linearising equations, finding slope and intercept, drawing best-fit lines and error bars, calculating gradient uncertainty. For IB, a whole branch on ‘Internal Assessment’ criteria exists; for CIE, practical paper requirements like significant figures, tabulating results, and evaluating limitations. Always link back to reliability and accuracy.
最后这张思维导图关注“实验”与“数据”。分支覆盖：测量不确定度（绝对、相对、百分比）；和差运算中绝对不确定度相加，积商运算中百分比不确定度相加；系统误差与随机误差对比。图像技能分支：方程的线性化，求斜率和截距，绘制最佳拟合线与误差棒，计算斜率不确定度。IB 还有一个完整分支针对“内部评估”标准；CIE 则关注实验卷要求，如有效数字、表格记录与局限性评估。始终联系回可靠性与准确度。
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