📚 Cramming Notes for IB & CCEA Physics: Last-Minute Revision | IB CCEA 物理考前冲刺笔记
This revision guide distills the essential concepts, formulas, and examiner tips for IB and CCEA Physics exams. Use it to rapidly refresh core topics, spot common pitfalls, and build confidence before the big day. Focus on understanding the principles behind each equation and practising with past papers to maximise your marks.
这份冲刺笔记浓缩了IB与CCEA物理考试的核心概念、公式和考官建议。帮助你快速回顾重点主题，发现常见错误，在考前建立信心。请聚焦于每个方程背后的原理，并结合往年真题练习，以获得最佳成绩。
1. Measurements & Uncertainties | 测量与不确定度
Accurate data recording and uncertainty propagation are fundamental skills. Every measured value must include an absolute or percentage uncertainty, and final results should reflect the weakest link in the measurement chain.
准确记录数据与处理不确定度的传递是基本技能。每个测量值都必须包含绝对或百分比不确定度，最终结果应反映出测量链中最薄弱的环节。
Record raw data with the same number of decimal places and quote absolute uncertainty as ± half the smallest scale division for analogue instruments, or ± the smallest digit for digital ones.
记录原始数据时保持相同的小数位数，对于模拟仪器，绝对不确定度取最小刻度的一半，例如 ±0.5 mm；对于数字仪器，取末位 ±1 个单位。
When adding or subtracting quantities, add absolute uncertainties. When multiplying or dividing, add percentage uncertainties. For a power relationship y = k xⁿ, the percentage uncertainty in y is n times the percentage uncertainty in x.
加减运算时，绝对不确定度相加。乘除运算时，百分比不确定度相加。对于幂函数关系 y = k xⁿ，y 的百分比不确定度是 x 的百分比不确定度的 n 倍。
Δy = |n| (Δx/x) × 100% (for y = k xⁿ)
Use error bars on graphs to find best-fit and worst-fit lines; the uncertainty in gradient or intercept can be estimated from the difference between the two lines.
在图表中使用误差棒绘制最佳拟合和最差拟合线；斜率或截距的不确定度可由两者之差估算。
2. Mechanics: Kinematics & Dynamics | 力学：运动学与动力学
Master the SUVAT equations for constant acceleration and free-body diagrams for force analysis. Distinguish between scalars and vectors, and always resolve forces into perpendicular components before applying Newton’s laws.
掌握匀加速运动的 SUVAT 方程以及受力分析中的隔离体图。区分标量与矢量，并在应用牛顿定律前务必将力沿垂直方向分解。
The four equations of motion for constant acceleration a, initial velocity u, final velocity v, displacement s, and time t are your tools for linear motion.
以下四个匀加速直线运动方程是解题基础，涉及加速度 a、初速度 u、末速度 v、位移 s 和时间 t。
v = u + a t s = u t + ½ a t² v² = u² + 2 a s s = ½ (u + v) t
Newton’s second law F = m a is a vector equation. Always draw a free-body diagram showing weight, normal reaction, friction, tension, and any applied forces.
牛顿第二定律 F = m a 是矢量方程。务必画出隔离体图，标明重力、法向反作用力、摩擦力、张力和其它外力。
Momentum p = m v is conserved in all collisions as long as no external resultant force acts. Impulse equals the change in momentum: F Δt = Δp.
动量 p = m v 在没有合外力作用的碰撞中守恒。冲量等于动量的变化：F Δt = Δp。
Work done W = F s cosθ; kinetic energy Eₖ = ½ m v²; gravitational potential energy Eₚ = m g h. Power is the rate of doing work: P = W/t = F v.
做功 W = F s cosθ；动能 Eₖ = ½ m v²；重力势能 Eₚ = m g h。功率是做功的速率：P = W/t = F v。
3. Thermal Physics | 热物理
Temperature is a measure of average kinetic energy of particles; heat is energy transferred due to temperature difference. Internal energy comprises both kinetic and potential components of all particles in a system.
温度是粒子平均动能的量度；热量是因温差而传递的能量。内能包括系统内所有粒子的动能和势能之和。
Specific heat capacity c relates energy transferred to temperature change: Q = m c Δθ. Specific latent heat L relates energy to phase change at constant temperature: Q = m L.
比热容 c 将传递的能量与温度变化关联：Q = m c Δθ。比潜热 L 将能量与恒温相变关联：Q = m L。
For an ideal gas, the equation of state is pV = nRT, where n is moles and R = 8.31 J mol⁻¹ K⁻¹. Kinetic theory links microscopic behaviour to macroscopic pressure: p = ⅓ ρ
理想气体状态方程为 pV = nRT，n 为摩尔数，R = 8.31 J mol⁻¹ K⁻¹。分子运动论将微观行为与宏观压强联系起来：p = ⅓ ρ
The average translational kinetic energy of a molecule is (3/2) k_B T, where k_B = 1.38 × 10⁻²³ J K⁻¹. This shows temperature is directly proportional to average kinetic energy.
分子的平均平动动能为 (3/2) k_B T，k_B = 1.38 × 10⁻²³ J K⁻¹。这表明温度与平均动能成正比。
The first law of thermodynamics ΔU = Q – W (work done BY the gas) is crucial. For isothermal expansion, ΔU = 0 so Q = W; for adiabatic, Q = 0 so ΔU = -W.
热力学第一定律 ΔU = Q – W（气体对外做功）至关重要。等温膨胀时 ΔU = 0 故 Q = W；绝热过程 Q = 0 故 ΔU = -W。
4. Waves & Oscillations | 波动与振动
Simple harmonic motion (SHM) occurs when acceleration is proportional to displacement from equilibrium and directed towards it: a = -ω² x. The period of a mass-spring system is T = 2π √(m/k), and for a simple pendulum T = 2π √(L/g).
简谐运动（SHM）的加速度与位移成正比且方向指向平衡位置：a = -ω² x。弹簧振子周期 T = 2π √(m/k)，单摆周期 T = 2π √(L/g)。
Energy in SHM continuously interchanges between kinetic and potential forms, but total energy remains constant: E_total = ½ m ω² A², where A is amplitude.
简谐运动中的能量在动能和势能之间不断转换，但总能量保持不变：E_total = ½ m ω² A²，A 为振幅。
For travelling waves, wave speed v = f λ. Intensity I is proportional to amplitude squared: I ∝ A². Remember that frequency remains constant when a wave passes from one medium to another; speed and wavelength change.
对于行波，波速 v = f λ。强度 I 与振幅的平方成正比：I ∝ A²。记住波从一种介质进入另一种时频率不变，波速和波长改变。
Standing waves form when two identical waves travel in opposite directions. Nodes have zero displacement, antinodes have maximum displacement. The distance between adjacent nodes is λ/2.
两列相同的波反向传播时形成驻波。波节处位移为零，波腹处位移最大。相邻波节间距为 λ/2。
Diffraction is most noticeable when the gap width is comparable to the wavelength. Single-slit minima occur at d sinθ = nλ, where d is slit width.
当缝隙宽度与波长相近时衍射最显著。单缝衍射极小值满足 d sinθ = nλ，d 为缝宽。
5. Electricity & Magnetism | 电学与磁学
Current I is the rate of flow of charge: I = ΔQ/Δt. Potential difference V is the energy per unit charge: V = W/Q. Resistance R = V/I, obeying Ohm’s law if the temperature remains constant and R is constant.
电流 I 是电荷流动的速率：I = ΔQ/Δt。电势差 V 是单位电荷的能量：V = W/Q。电阻 R = V/I，若温度恒定且 R 不变则遵循欧姆定律。
Resistivity ρ is a material property: R = ρ L/A. In a series circuit, total resistance R_total = R₁ + R₂ + …; in parallel, 1/R_total = 1/R₁ + 1/R₂ + ….
电阻率 ρ 是材料特性：R = ρ L/A。串联电路总电阻 R_total = R₁ + R₂ + …；并联电路 1/R_total = 1/R₁ + 1/R₂ + …。
Kirchhoff’s first law states that total current entering a junction equals total current leaving. Second law: around any closed loop, sum of emfs equals sum of p.d.s (Σ ε = Σ IR).
基尔霍夫第一定律：流入节点的总电流等于流出节点的总电流。第二定律：沿任一闭合回路，电动势的代数和等于各段电压的代数和 (Σ ε = Σ IR)。
Magnetic force on a moving charge F = q v B sinθ, direction given by Fleming’s left-hand rule (for conventional current). On a current-carrying wire, F = B I L sinθ.
运动电荷在磁场中的受力 F = q v B sinθ，方向由左手定则判定（针对正电荷）。通电导线受力 F = B I L sinθ。
Magnetic flux φ = B A cosθ; flux density B is measured in tesla. Faraday’s law: induced emf ε = -N Δφ/Δt. Lenz’s law gives the direction of induced current, which opposes the change causing it.
磁通量 φ = B A cosθ；磁通密度 B 的单位为特斯拉。法拉第定律：感应电动势 ε = -N Δφ/Δt。楞次定律确定感应电流方向，即阻碍引起感应的变化。
6. Circular Motion & Gravitation | 圆周运动与引力
An object moving in a circle at constant speed experiences centripetal acceleration a = v²/r = ω² r, directed towards the centre. The centripetal force is F = m v²/r = m ω² r.
物体做匀速圆周运动时具有向心加速度 a = v²/r = ω² r，方向指向圆心。向心力 F = m v²/r = m ω² r。
Newton’s law of universal gravitation: F = G M m / r², where G = 6.67 × 10⁻¹¹ N m² kg⁻². This force provides the centripetal force for orbiting bodies.
牛顿万有引力定律：F = G M m / r²，G = 6.67 × 10⁻¹¹ N m² kg⁻²。这个力为绕轨天体提供向心力。
Gravitational field strength g = F/m = G M / r². At the Earth’s surface, g ≈ 9.81 N kg⁻¹. Field lines point towards the mass creating the field.
引力场强度 g = F/m = G M / r²。地球表面 g ≈ 9.81 N kg⁻¹。引力场线指向产生场的质量中心。
Geostationary orbits have a period of 24 hours, lie in the equatorial plane, and orbit in the same direction as Earth’s rotation. Use T² = (4π²/GM) r³ to find the required radius.
地球同步轨道周期为 24 小时，轨道在赤道面上，且与地球自转方向相同。利用 T² = (4π²/GM) r³ 可计算所需轨道半径。
7. Atomic, Nuclear & Particle Physics | 原子、核与粒子物理
The nuclear model: a small, dense, positively charged nucleus surrounded by electrons. Nuclei are held together by the strong nuclear force, which is short-range and charge-independent.
原子核模型：微小、致密、带正电的原子核被电子包围。原子核由强核力束缚，该力短程且与电荷无关。
Radioactive decay is random and exponential: N = N₀ e^{-λt}, where λ is the decay constant. Half-life t₁/₂ = ln2 / λ. Activity A = λ N.
放射性衰变是随机且呈指数规律的：N = N₀ e^{-λt}，λ 为衰变常量。半衰期 t₁/₂ = ln2 / λ。活度 A = λ N。
Alpha decay reduces Z by 2 and A by 4. Beta-minus decay converts a neutron to a proton, emitting an electron and antineutrino. Beta-plus decay emits a positron and neutrino.
α 衰变使原子序数减 2、质量数减 4。β⁻ 衰变中中子变为质子，发射电子和反中微子。β⁺ 衰变发射正电子和中微子。
In nuclear reactions, mass-energy is conserved: E = m c². The mass defect and binding energy per nucleon determine stability; iron-56 has the highest binding energy per nucleon.
核反应中质能守恒：E = m c²。质量亏损和平均结合能决定原子核稳定性；铁-56 的平均结合能最大。
Fusion combines light nuclei; fission splits heavy nuclei. Both release energy. Chain reactions in uranium-235 require a critical mass and neutron moderation in thermal reactors.
聚变将轻核结合；裂变将重核分裂。两者都释放能量。铀-235 的链式反应需要达到临界质量，并在热中子反应堆中使用慢化剂。
8. Waves Optics: Interference & Polarisation | 波动光学：干涉与偏振
Young’s double-slit experiment demonstrates interference. Bright fringes occur at d sinθ = nλ; fringe spacing Δy = λ D / d, where D is the distance to the screen and d is slit separation.
杨氏双缝实验展示了干涉现象。亮条纹满足 d sinθ = nλ；条纹间距 Δy = λ D / d，D 为屏幕距双缝的距离，d 为缝距。
Coherent sources have constant phase difference and same frequency. White light produces a central white fringe with coloured fringes on either side because λ varies with colour.
相干光源具有恒定相位差和相同频率。白光产生中央白色条纹，两侧为彩色条纹，因为不同颜色波长不同。
Thin-film interference arises from reflections at the top and bottom surfaces of a film. For constructive interference in reflected light from a film in air, 2 n t = (m + ½) λ.
薄膜干涉源于薄膜上下表面反射光的光程差。空气中薄膜的反射光相长干涉条件为 2 n t = (m + ½) λ。
Polarisation is evidence that light is a transverse wave. When unpolarised light passes through a polariser, intensity is halved. For two polarisers at angle θ, Malus’s law gives I = I₀ cos²θ.
偏振现象证实光是横波。非偏振光通过偏振片后强度减半。当两个偏振片夹角为 θ 时，马吕斯定律给出 I = I₀ cos²θ。
Brewster’s angle: when reflected and refracted rays are perpendicular, reflected light is fully polarised parallel to the surface. tan θ_B = n.
布儒斯特角：当反射光线与折射光线垂直时，反射光完全偏振且平行于表面。tan θ_B = n。
9. Electromagnetic Induction & AC | 电磁感应与交流电
Alternating current varies sinusoidally with time: V = V₀ sin(ωt) and I = I₀ sin(ωt). Root mean square (rms) values relate to peak values: V_rms = V₀/√2, I_rms = I₀/√2.
交流电随时间正弦变化：V = V₀ sin(ωt)，I = I₀ sin(ωt)。均方根值与峰值关系为 V_rms = V₀/√2，I_rms = I₀/√2。
Transformers change AC voltages using mutual induction. For an ideal transformer, V_s/V_p = N_s/N_p = I_p/I_s. Power is conserved: V_p I_p = V_s I_s.
变压器利用互感改变交流电压。理想变压器满足 V_s/V_p = N_s/N_p = I_p/I_s。功率守恒：V_p I_p = V_s I_s。
Generators convert mechanical energy to electrical energy. In a rotating coil, the induced emf varies as ε = N B A ω sin(ωt). The maximum emf is ε₀ = N B A ω.
发电机将机械能转化为电能。旋转线圈中感应电动势按 ε = N B A ω sin(ωt) 变化。最大电动势 ε₀ = N B A ω。
Self-inductance L relates induced emf to rate of change of current: ε = -L dI/dt. Energy stored in an inductor is ½ L I². LCR circuits exhibit resonance when ω₀ = 1/√(LC).
自感 L 将感应电动势与电流变化率关联：ε = -L dI/dt。电感储存能量为 ½ L I²。LCR 电路在 ω₀ = 1/√(LC) 时发生谐振。
10. Energy, Power & Climate Change | 能源、功率与气候变化
Sankey diagrams show energy transfers to scale; the width of each arrow represents the amount of energy. Efficiency = useful output power / total input power.
桑基图按比例展示能量转移；箭头宽度代表能量多少。效率 = 有用输出功率 / 总输入功率。
Renewable sources include solar, wind, hydroelectric, tidal, geothermal, and biomass. Non-renewable sources include fossil fuels and nuclear fission. Each has advantages and disadvantages regarding cost, reliability, and environmental impact.
可再生能源包括太阳能、风能、水能、潮汐能、地热能和生物质能。不可再生能源包括化石燃料和核裂变。各种能源在成本、可靠性和环境影响上各有利弊。
Black-body radiation peaks at a wavelength inversely proportional to temperature: λ_max T = 2.9 × 10⁻³ m K (Wien’s law). Total power radiated P = e σ A T⁴ (Stefan-Boltzmann law).
黑体辐射峰值波长与温度成反比：λ_max T = 2.9 × 10⁻³ m K（维恩位移定律）。总辐射功率 P = e σ A T⁴（斯特藩-玻尔兹曼定律）。
The Earth’s energy balance depends on incoming solar radiation, albedo, and the greenhouse effect. Enhanced greenhouse effect due to CO₂ and methane leads to global warming.
地球能量平衡取决于入射太阳辐射、反照率和温室效应。因 CO₂ 和甲烷等导致的增强温室效应引起全球变暖。
Examiners often ask you to evaluate strategies to reduce carbon emissions, such as carbon capture, improved efficiency, and switching to renewables. Support arguments with quantitative estimates.
考官常要求评价减少碳排放的策略，如碳捕集、提高能效和转向可再生能源。论述时务必引用量化估算。
11. Exam Technique & Common Pitfalls | 考试技巧与常见误区
Always read the stem carefully and underline command terms: ‘State’, ‘Explain’, ‘Calculate’, ‘Suggest’. Show all working for calculations; even a correct answer can lose marks if steps are missing.
仔细阅读题干，划出指令词：如“陈述”“解释”“计算”“提出”。计算题务必展示所有步骤；即使答案正确也可能因缺少步骤而失分。
Pay attention to significant figures: typically give final answers to 2 or 3 s.f., matching the least precise data. Do not forget units; missing units often cost a mark.
注意有效数字：通常最终答案保留 2 或 3 位有效数字，与最不精确的数据一致。别忘了写单位，漏写单位常导致扣分。
In practical-based questions, comment on repeat readings, anomalies, and precautions like avoiding parallax error or insulating thermal apparatus.
在实验相关题目中，要提及重复读数、异常值以及避免视差或对热学仪器进行隔热的预防措施。
When answering long questions on applications or ‘how science works’, structure your response: state the physics principle, apply it to the context, and then discuss implications or limitations.
回答有关应用或“科学工作方式”的长问题时，请结构化作答：先陈述物理原理，再将其应用在情景中，然后讨论影响或局限性。
Common mistake: confusing electric field strength E = F/q with gravitational field strength g = F/m. They are analogous but differ in direction and the fact that mass does not repel.
常见误区：混淆电场强度 E = F/q 与引力场强度 g = F/m。两者类似，但方向不同，且质量不会排斥。
Another trap: using v = f λ for standing waves incorrectly; remember that for a string fixed at both ends, the fundamental frequency corresponds to λ = 2L, not L.
另一个陷阱：驻波中错误地使用 v = f λ；记住两端固定的弦，基频对应的波长为 λ = 2L，而非 L。
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