IB OCR Physics: Last-Minute Revision Notes | IB OCR 物理：考前冲刺笔记

📚 IB OCR Physics: Last-Minute Revision Notes | IB OCR 物理：考前冲刺笔记

This article distils the essential concepts, equations and exam techniques for the IB and OCR Physics specifications. It is designed as a rapid-fire revision aid to help you consolidate understanding and avoid common pitfalls just before the exam.

本文浓缩了 IB 和 OCR 物理课程的核心概念、方程与应试技巧，是一份考前快速复习指南，帮助你巩固理解、避开常见失分点。

1. Measurements and Uncertainties | 测量与不确定度

Precision refers to the closeness of repeated readings, while accuracy describes how close a measurement is to the true value. Systematic errors affect accuracy; random errors affect precision.

精密度指多次读数之间的接近程度，准确度则指测量值与真值的接近程度。系统误差影响准确度，随机误差影响精密度。

When combining uncertainties, for addition or subtraction add absolute uncertainties; for multiplication or division add percentage uncertainties. The final answer should be quoted to the same number of significant figures as the least precise measurement.

合成不确定度时，加减运算使用绝对不确定度相加；乘除运算使用相对（百分比）不确定度相加。最终答案的有效数字位数应与最不精确的测量值一致。

2. Kinematics | 运动学

The SUVAT equations apply only when acceleration is constant. They link displacement s, initial velocity u, final velocity v, acceleration a and time t.

SUVAT 方程仅适用于加速度恒定的情况，它们将位移 s、初速度 u、末速度 v、加速度 a 和时间 t 联系起来。

v = u + at

v² = u² + 2as

Always define a positive direction before using vector quantities. For projectile motion, resolve velocity into horizontal and vertical components; horizontal motion has constant velocity, vertical motion has constant acceleration g = 9.81 m s⁻².

使用矢量之前务必规定正方向。对于抛体运动，将速度分解为水平与竖直分量；水平方向为匀速运动，竖直方向具有恒定加速度 g = 9.81 m s⁻²。

Gradient of a displacement–time graph gives velocity; gradient of a velocity–time graph gives acceleration; area under a velocity–time graph gives displacement.

位移-时间图线的斜率表示速度；速度-时间图线的斜率表示加速度；速度-时间图线下的面积表示位移。

3. Dynamics and Newton’s Laws | 动力学与牛顿定律

Newton’s First Law: an object remains at rest or in uniform motion unless acted upon by a net external force. Newton’s Second Law: F = ma, where force is measured in newtons. Newton’s Third Law: if body A exerts a force on body B, B exerts an equal and opposite force on A.

牛顿第一定律：若无净外力作用，物体保持静止或匀速直线运动状态。牛顿第二定律：F = ma，力的单位为牛顿。牛顿第三定律：若物体 A 对 B 施力，B 同时对 A 施加大小相等、方向相反的力。

Free-body diagrams must show all forces acting on a single body. The net force is the vector sum. When drawing, label forces clearly and do not include resultant force on the same diagram.

受力图必须画出作用在同一物体上的所有力。合力为各力的矢量和。作图时清楚地标出所有力，不要把合力也画在同一图上。

For objects in equilibrium, the net force and net torque are both zero. This enables solving unknown forces by resolving components in perpendicular directions.

处于平衡状态的物体，合外力与合力矩均为零。借此可以通过分解垂直方向上的分力求解未知力。

4. Work, Energy and Power | 功、能与功率

Work done W = Fs cosθ, where θ is the angle between force and displacement. Energy is the capacity to do work; the principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed.

做功 W = Fs cosθ，θ 为力与位移的夹角。能量是做功的本领；能量守恒定律指出能量既不能创生也不能消灭，只能转移或转化。

Kinetic energy Eₖ = ½mv², gravitational potential energy Eₚ = mgΔh. In a closed system with no friction, the sum of Eₖ and Eₚ remains constant.

动能 Eₖ = ½mv²，重力势能 Eₚ = mgΔh。若无摩擦的封闭系统中，动能与重力势能之和恒定。

Power P = W/t = Fv for constant force parallel to velocity. Efficiency = useful output power / total input power, often quoted as a percentage.

功率 P = W/t，在力与速度平行且恒定时 P = Fv。效率 = 有用输出功率 / 总输入功率，常以百分比表示。

5. Momentum and Impulse | 动量与冲量

Momentum p = mv is a vector. Impulse J = FΔt = Δp, equal to the area under a force–time graph. The law of conservation of momentum states that total momentum in a closed system remains constant in the absence of external forces.

动量 p = mv 是矢量。冲量 J = FΔt = Δp，等于力-时间图线下的面积。动量守恒定律指出，在无外力的封闭系统中总动量保持恒定。

For elastic collisions, both momentum and kinetic energy are conserved. For inelastic collisions, only momentum is conserved while kinetic energy is dissipated as heat or deformation.

弹性碰撞中动量和动能均守恒。非弹性碰撞中仅动量守恒，部分动能转化为热能或变形能。

Two-dimensional collisions are analysed by resolving momentum into perpendicular directions and applying conservation separately along each axis.

分析二维碰撞时，将动量分解到互相垂直的两个方向上，并对每个坐标轴分别应用动量守恒。

6. Circular Motion and Gravitation | 圆周运动与万有引力

An object moving in a circle at constant speed has centripetal acceleration directed towards the centre: a = v² / r = ω²r, where v = ωr. The centripetal force is F = mv² / r = mω²r.

做匀速圆周运动的物体具有指向圆心的向心加速度：a = v² / r = ω²r，其中 v = ωr。向心力为 F = mv² / r = mω²r。

Newton’s Law of Gravitation: F = G M m / r². Gravitational field strength g = F/m = GM / r². Near Earth’s surface g ≈ 9.81 N kg⁻¹.

牛顿万有引力定律：F = G M m / r²。引力场强度 g = F/m = GM / r²。在地球表面附近 g ≈ 9.81 N kg⁻¹。

For satellites, equate gravitational force to centripetal force to derive orbital speed v = √(GM / r) and period T² ∝ r³ (Kepler’s Third Law). Geostationary satellites have a period of 24 hours and orbit in the equatorial plane.

对于卫星，令万有引力等于向心力可推导出轨道速率 v = √(GM / r) 和周期 T² ∝ r³（开普勒第三定律）。地球同步卫星的周期为 24 小时，轨道位于赤道平面内。

7. Oscillations and Waves | 振动与波

Simple harmonic motion (SHM) occurs when acceleration is proportional to displacement from equilibrium and directed opposite: a = -ω²x. The period T = 2π / ω. For a mass–spring system T = 2π√(m/k); for a simple pendulum T = 2π√(L/g).

简谐运动发生时，加速度与偏离平衡位置的位移成正比且方向相反：a = -ω²x。周期 T = 2π / ω。对于弹簧振子 T = 2π√(m/k)；对于单摆 T = 2π√(L/g)。

Waves transfer energy without net transport of matter. Transverse waves have oscillations perpendicular to propagation; longitudinal waves have oscillations parallel. Key parameters: wavelength λ, frequency f, speed v = fλ.

波传递能量而不引起介质的净迁移。横波的振动方向垂直于传播方向；纵波的振动方向平行于传播方向。关键参数：波长 λ、频率 f、波速 v = fλ。

Phase difference is the fraction of a cycle by which one oscillation lags behind another. Constructive interference occurs when path difference is nλ; destructive when path difference is (n + ½)λ.

相位差是一个振动落后于另一个振动的周期比。当波程差为 nλ 时发生相长干涉；为 (n + ½)λ 时发生相消干涉。

Standing waves form when two identical waves travel in opposite directions. Nodes are points of zero displacement; antinodes have maximum displacement. In pipes, open ends are pressure nodes/displacement antinodes; closed ends are displacement nodes/pressure antinodes.

驻波由两个相同波沿相反方向传播叠加形成。波节位移为零；波腹位移最大。在管乐器中，开口端为压力波节/位移波腹；闭口端为位移波节/压力波腹。

8. Electricity and DC Circuits | 电学与直流电路

Current I = ΔQ / Δt. In a conductor, I = nAvq, where n is charge carrier density. Ohm’s Law V = IR holds for ohmic conductors at constant temperature. Resistance R = ρL/A depends on resistivity, length and cross-sectional area.

电流 I = ΔQ / Δt。在导体中 I = nAvq，n 为载流子密度。欧姆定律 V = IR 适用于恒温下的欧姆导体。电阻 R = ρL/A 取决于电阻率、长度和横截面积。

Potential divider equation: Vout = Vin × (R₂ / (R₁ + R₂)). This is used with sensors like LDRs and thermistors to trigger circuits. A thermistor’s resistance decreases with temperature; an LDR’s resistance decreases with light intensity.

分压公式：Vout = Vin × (R₂ / (R₁ + R₂))，常用于与光敏电阻和热敏电阻等传感器相连的触发电路。热敏电阻的阻值随温度升高而减小；光敏电阻的阻值随光照增强而减小。

EMF ε is the energy supplied per unit charge. Internal resistance r causes terminal pd V = ε – Ir. Power dissipated is P = IV = I²R = V²/R.

电动势 ε 是电源将其他形式能转化为每单位电荷电能的本领。内阻 r 导致路端电压 V = ε – Ir。焦耳热功率为 P = IV = I²R = V²/R。

Kirchhoff’s laws: junction rule – sum of currents entering a junction equals sum leaving; loop rule – sum of emfs equals sum of pd s around any closed loop.

基尔霍夫定律：节点电流定律 – 流入节点的电流之和等于流出节点的电流之和；回路电压定律 – 沿任一闭合回路，电动势的代数和等于各段电压降的代数和。

9. Magnetism and Electromagnetic Induction | 磁学与电磁感应

Magnetic flux density B is measured in tesla. Force on a current-carrying wire F = BIL sinθ; force on a moving charge F = Bqv sinθ. Fleming’s left-hand rule gives the direction of force.

磁感应强度 B 的单位为特斯拉。载流导线在磁场中受力 F = BIL sinθ；运动电荷受力 F = Bqv sinθ。弗莱明左手定则给出力的方向。

Faraday’s Law: induced emf is proportional to rate of change of magnetic flux linkage. ε = -N ΔΦ / Δt, where Φ = BA cosθ. Lenz’s Law states the induced current opposes the change that caused it.

法拉第定律：感应电动势与磁链变化率成正比，ε = -N ΔΦ / Δt，其中 Φ = BA cosθ。楞次定律表明感应电流的方向总是阻碍引起感应电流的磁通量变化。

Transformers change voltages: Vₛ / Vₚ = Nₛ / Nₚ. For an ideal transformer, power input equals power output, so IₚVₚ = IₛVₛ. Step-up transformers increase voltage and decrease current, reducing transmission losses.

变压器改变电压：Vₛ / Vₚ = Nₛ / Nₚ。理想变压器输入功率等于输出功率，故 IₚVₚ = IₛVₛ。升压变压器升高电压、降低电流，从而减少输电线上的能量损耗。

10. Thermal Physics | 热物理

Absolute zero (0 K = -273°C) is the temperature at which particles have minimum kinetic energy. The gas laws relate pressure p, volume V and temperature T for a fixed mass of ideal gas: pV = nRT = NkₐT.

绝对零度 (0 K = -273°C) 是粒子动能最低的温度。气体实验定律联系了一定质量理想气体的压强 p、体积 V 和热力学温度 T：pV = nRT = NkₐT。

For an ideal gas, the internal energy is entirely kinetic. The average kinetic energy per particle Eₖ = (3/2)kₐT. Real gases deviate at high pressure and low temperature due to intermolecular forces and finite molecular size.

理想气体的内能全部为动能。每个粒子的平均动能 Eₖ = (3/2)kₐT。真实气体在高压、低温时因分子间作用力和分子自身体积而产生偏离。

Specific heat capacity c = Q / (mΔθ); specific latent heat L = Q / m during phase change. When substance changes state, temperature remains constant while energy is absorbed or released.

比热容 c = Q / (mΔθ)；相变时比潜热 L = Q / m。物质发生物态变化时，温度保持恒定而持续吸收或释放能量。

11. Atomic, Nuclear and Particle Physics | 原子、核与粒子物理

Rutherford’s gold foil experiment showed that most of the atom is empty space with a tiny, dense, positively charged nucleus. Nuclear radius R = r₀ A^{1/3}, where A is the mass number.

卢瑟福金箔实验表明原子内部绝大部分是空的，中心存在极小、高密度、带正电的原子核。核半径 R = r₀ A^{1/3}，A 为质量数。

The strong nuclear force binds nucleons together, acting over very short distances. In nuclear reactions, mass–energy equivalence E = mc² applies; binding energy is the energy required to separate a nucleus into its constituent nucleons.

强核力在极短距离内将核子束缚在一起。核反应中质能方程 E = mc² 适用；结合能是将原子核分解为单个核子所需的能量。

Radioactive decay is a random process. Activity A = λN. Decay law: N = N₀ e^{-λt}. Half-life t₁/₂ = ln2 / λ. Alpha particles are helium nuclei, beta particles are high-speed electrons (or positrons), and gamma radiation is high-frequency electromagnetic waves.

放射性衰变是随机过程。放射性活度 A = λN。衰变规律：N = N₀ e^{-λt}。半衰期 t₁/₂ = ln2 / λ。α 粒子为氦核，β 粒子为高速电子（或正电子），γ 射线为高频电磁波。

12. Quantum Physics and the Photoelectric Effect | 量子物理与光电效应

Photoelectric effect demonstrates the particle nature of light. Electrons are emitted from a metal surface when the incident photon energy hf exceeds the work function Φ. Maximum kinetic energy: KEₘₐₓ = hf – Φ.

光电效应显示了光的粒子性。当入射光子能量 hf 大于金属的逸出功 Φ 时，电子从金属表面逸出。最大动能：KEₘₐₓ = hf – Φ。

Increasing intensity (more photons) increases the photocurrent but does not affect the maximum kinetic energy. There is a threshold frequency f₀ = Φ / h below which no electrons are emitted, regardless of intensity.

增加光强（光子数目增多）会增大光电流，但不改变电子最大动能。存在一个截止频率 f₀ = Φ / h，低于此频率无论光强多大均无电子发射。

De Broglie wavelength λ = h / p links particle and wave properties. Wave–particle duality means all particles can exhibit interference and diffraction under appropriate conditions; electrons show diffraction patterns through a thin crystal.

德布罗意波长 λ = h / p 将粒子性与波动性联系起来。波粒二象性意味着在适当条件下所有粒子都可表现出干涉和衍射；电子通过薄晶体可产生衍射图样。

Emission and absorption spectra provide evidence for discrete atomic energy levels. Transitions between levels involve photons of energy E = hf = hc / λ, giving characteristic line spectra.

发射光谱和吸收光谱为原子具有分立能级提供了证据。电子在能级间跃迁时吸收或发射光子，能量 E = hf = hc / λ，形成特征线状光谱。

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）