IB & AQA Physics: Last-Minute Crash Revision Notes | IB AQA 物理考前冲刺笔记

📚 IB & AQA Physics: Last-Minute Crash Revision Notes | IB AQA 物理考前冲刺笔记

This guide consolidates the most vital concepts, formulas, and problem-solving strategies shared by both the IB Physics (SL/HL) and AQA A-level Physics syllabuses. Use it in the final days before your exam to sharpen recall, avoid common pitfalls, and boost confidence. Every section pairs essential theory with immediately applicable equations so you can move straight from reading to practice.

这份指南浓缩了 IB 物理（SL/HL）与 AQA A-level 物理课程中最关键的概念、公式和解题策略。在考前最后几天使用它来强化记忆、避开常见陷阱并提升信心。每个小节都将核心理论与可直接使用的方程式配对，让你读完就能直接投入练习。

1. Kinematics and Straight-Line Motion | 运动学与直线运动

Mastering the SUVAT equations is non‑negotiable for both IB and AQA. They describe uniform acceleration along a straight line, linking displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). Always define a positive direction before substituting values; vectors in the opposite direction must carry a negative sign. IB data booklet provides these equations, while AQA expects you to recall and apply them fluently.

掌握 SUVAT 方程对 IB 和 AQA 考生来说都是必须的。它们描述匀变速直线运动，关联位移 s、初速度 u、末速度 v、加速度 a 和时间 t。代入数值前务必先规定正方向；与正方向相反的矢量必须带负号。IB 数据手册会提供这些方程，而 AQA 希望你能熟练记住并应用它们。

v = u + at s = ut + ½at² v² = u² + 2as s = ½(u + v)t

In free‑fall problems, replace a with g = 9.81 m s⁻² and pay close attention to signs: an object thrown upwards has u positive and a = –g. IB often embeds free‑fall into projectile motion, while AQA may test it in multi‑step mechanics scenarios. A velocity‑time graph gives displacement as area, acceleration as gradient; make sure you can switch between graphical and algebraic methods.

在自由落体问题中，将 a 替换为 g = 9.81 m s⁻² 并特别注意符号：竖直上抛物体的 u 为正，a = –g。IB 常把自由落体融入抛体运动，AQA 则在多步骤力学情境中考查。速度‑时间图将位移表示为面积、加速度表示为斜率；务必确保自己能游刃有余地在图解法和代数法间切换。

2. Forces and Newton’s Laws | 力与牛顿定律

Newton’s three laws underpin every mechanics question. The Second Law, F = ma, is a vector equation: resultant force determines acceleration. When analysing a system, draw a free‑body diagram showing all forces acting on a single body, then resolve them into perpendicular components. The normal reaction is not simply mg on an incline — it becomes mg cosθ. Friction is f ≤ μR, with kinetic friction f = μₖR.

牛顿三定律是所有力学题的基础。第二定律 F = ma 是矢量方程：合外力决定加速度。分析系统时，先画单个物体的受力图，展示所有作用力，再将其分解为垂直分量。斜面上的法向反作用力不是简单的 mg，而是 mg cosθ。摩擦力满足 f ≤ μR，而动摩擦力 f = μₖR。

ΣF = ma F(friction) = μR Tension transmits force without change in ideal strings

Connected‑body problems require writing F = ma for each mass and solving simultaneously. In IB, this often appears in Paper 2 extended‑response questions; AQA uses them across mechanics sections. Equilibrium occurs when ΣF = 0 — a condition that applies to both stationary objects and those moving with constant velocity. Do not forget that air resistance is a velocity‑dependent force, relevant for terminal velocity discussions.

连接体问题需要对每个物体分别列出 F = ma 并联立求解。IB 常在试卷二的拓展题中出现；AQA 则在力学各板块均有使用。平衡状态意味着 ΣF = 0 —— 这一条件既适用于静止物体，也适用于匀速运动的物体。别忘了空气阻力是速度相关的力，这与收尾速度的讨论密切相关。

3. Energy, Work and Power | 能量、功与功率

The work‑energy theorem states that net work done equals the change in kinetic energy: W = ΔEₖ. Work done by a constant force is F s cosθ. Gravitational potential energy near Earth’s surface is Eₚ = mgh, but IB also requires the universal form Eₚ = –GMm/r for varying gravitational fields. The principle of conservation of energy allows you to equate initial and final energy stores, provided you account for work done against non‑conservative forces.

功能原理指出，合力做的功等于动能变化量：W = ΔEₖ。恒力做功为 F s cosθ。地表附近的重力势能为 Eₚ = mgh，但 IB 还要求掌握变化引力场中的普遍形式 Eₚ = –GMm/r。能量守恒定律允许你将初始与末态能量储存量设为相等，前提是你要计入克服非保守力所做的功。

Eₖ = ½mv² Eₚ = mgh Power = W/t = Fv

Power is the rate of energy transfer; the expression P = Fv applies when a constant force moves an object at constant speed in its direction. Efficiency is the ratio of useful output power to input power. Both boards test the ability to calculate energy dissipated in braking, springs, and electrical heating. For springs, elastic potential energy is E = ½k(Δx)² — remember that a spring stores energy in both extension and compression.

功率是能量传递的速率；当恒力沿速度方向推动物体匀速运动时，可使用 P = Fv。效率指有用输出功率与输入功率之比。两大考试局都会考查制动、弹簧和电热中的能量耗散计算。对于弹簧，弹性势能为 E = ½k(Δx)² —— 记得弹簧在拉伸和压缩时都能储存能量。

4. Momentum and Impulse | 动量与冲量

Momentum p = mv is a vector. The impulse J = Δp = F Δt explains how forces change motion over short intervals; area under a force‑time graph gives impulse. Conservation of momentum holds in isolated systems, making it the core tool for collisions and explosions. In two‑dimensional collisions, resolve momentum along perpendicular axes and conserve separately for each direction; IB requires competence in 2D collisions, while AQA usually restricts to one dimension.

动量 p = mv 是一个矢量。冲量 J = Δp = F Δt 说明了短时间内力如何改变运动；力‑时间图线下面积即为冲量。在孤立系统中动量守恒，这使其成为解决碰撞与爆炸问题的核心工具。在二维碰撞中，要将动量沿垂直坐标轴分解并分别沿各方向守恒；IB 要求掌握二维碰撞，AQA 通常只限于一维。

p = mv Δp = F Δt m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Elastic collisions conserve kinetic energy; inelastic collisions do not, but momentum is still conserved. In a perfect inelastic collision, objects stick together and share a common final velocity. IB candidates should be able to link momentum conservation to the rate of change of momentum in rockets (thrust = vₑ × dm/dt). AQA also examines the relationship between momentum and safety devices such as airbags and crumple zones, which extend impact time to reduce force.

弹性碰撞动能守恒；非弹性碰撞不守恒，但动量依旧守恒。完全非弹性碰撞中，物体粘在一起并以共同速度运动。IB 考生还应能够联系动量守恒与火箭问题中的动量变化率（推力 = vₑ × dm/dt）。AQA 同样考查动量与安全装置（如安全气囊和溃缩区）之间的关系——通过延长碰撞时间来减小作用力。

5. Circular Motion | 圆周运动

An object moving in a circle at constant speed still experiences acceleration because its velocity direction changes; this centripetal acceleration points toward the centre. Both syllabuses require you to identify the actual force providing centripetal force — tension, gravity, friction, or the normal reaction — and set it equal to mv²/r or mω²r. Never add a separate “centripetal force” to your free‑body diagram; it is always the resultant of real forces.

一个匀速做圆周运动的物体依然有加速度，因其速度方向不断改变；这个向心加速度指向圆心。两大课程均要求你辨认提供向心力的实际力——张力、重力、摩擦力或法向反作用力——并将其设为 mv²/r 或 mω²r。绝不要在受力图中额外添加一个“向心力”；它始终是真实作用力的合力。

a = v²/r = ω²r F(centripetal) = mv²/r = mω²r v = ωr

Angular velocity ω (rad s⁻¹) links strongly with periodic time T and frequency f: ω = 2π/T = 2πf. Banked tracks and conical pendulums are classic exam applications: resolve forces along vertical and radial directions, use the fact that vertical acceleration is zero, and horizontal resultant provides mv²/r. IB frequently sets these in Paper 1 multiple‑choice, while AQA uses them in structured long questions.

角速度 ω（rad s⁻¹）与周期 T 和频率 f 紧密关联：ω = 2π/T = 2πf。弯道设计与圆锥摆是经典的考题应用：沿竖直和径向分解力，利用竖直方向加速度为零、水平方向合力提供 mv²/r 来求解。IB 常在试卷一选择题中设置此类题目，AQA 则将其用于结构化长问题中。

6. Gravitational Fields | 引力场

Newton’s law of gravitation describes the force between point masses: F = GMm/r². Gravitational field strength g at a point is the force per unit mass and follows an inverse‑square law outside spherical masses. Both IB and AQA require you to derive Kepler’s third law for circular orbits by equating gravitational force to centripetal force, yielding T² ∝ r³. Be prepared to discuss geostationary satellites and how their orbital period of 24 hours determines radius.

牛顿引力定律描述了质点间的引力：F = GMm/r²。某点的引力场强度 g 是单位质量所受的力，且在球形物体外部遵循平方反比律。IB 和 AQA 都要求你通过让引力等于向心力来推导出圆轨道的开普勒第三定律，即 T² ∝ r³。准备好讨论地球同步卫星，以及其 24 小时的轨道周期如何决定轨道半径。

F = GMm/r² g = GM/r² T² = (4π²/GM) r³

Gravitational potential V = –GM/r is a scalar, and the work done in moving a mass in a field is m ΔV. Equipotential surfaces are spherical; field lines are radial. In IB, comparing gravitational and electric fields is a favourite synoptic topic; AQA similarly links gravitation and electrostatics. Remember that escape velocity vₑ = √(2GM/R) is independent of the escaping mass and can be derived by equating kinetic energy to the magnitude of gravitational potential energy.

引力势 V = –GM/r 是标量，在引力场中移动质量所做的功为 m ΔV。等势面为球面；场线沿径向。在 IB 中，比较引力场与电场是常见的综合性话题；AQA 同样会将万有引力与静电联系起来。记住逃逸速度 vₑ = √(2GM/R) 与逃逸物体的质量无关，它可以通过让动能等于引力势能的绝对值推导出来。

7. Simple Harmonic Motion | 简谐运动

SHM occurs when the restoring force is proportional to displacement and directed toward equilibrium: F = –kx. The defining equation is a = –ω²x. Solutions are sinusoidal: x = x₀ sin(ωt) or x = x₀ cos(ωt), with velocity and acceleration obtained by differentiation or by using v = ±ω √(x₀² – x²) and a = –ω²x. IB candidates must recognise energy‑position graphs; AQA likewise expects you to sketch kinetic, potential, and total energy relationships.

当回复力与位移成正比并指向平衡位置时，物体做简谐运动：F = –kx。其定义方程为 a = –ω²x。解是正弦函数：x = x₀ sin(ωt) 或 x = x₀ cos(ωt)，速度与加速度可通过求导或使用 v = ±ω √(x₀² – x²) 及 a = –ω²x 得到。IB 考生必须能识别能量‑位移图；AQA 同样期望你能画出动能、势能和总能量之间的关系。

a = –ω²x T = 2π/ω for mass‑spring T = 2π√(m/k) for pendulum T = 2π√(l/g)

Pendulum period assumes small amplitudes. Damping reduces amplitude over time; light damping is often modelled with an exponential envelope. Forced oscillations and resonance occur when driving frequency matches natural frequency. In IB, resonance is linked to bridge collapse and musical instruments; AQA includes resonance in both mechanical and electrical systems (LCR circuits). Phase difference between displacement and forcing is a key conceptual point.

单摆周期假设振幅很小。阻尼会使振幅随时间衰减；轻阻尼常用指数包络线建模。当驱动力频率等于固有频率时发生受迫振动与共振。IB 中将共振与桥梁坍塌和乐器联系起来；AQA 在力学与电学系统（LCR 电路）中均涵盖共振。位移和驱动力之间的相位差是重要的概念点。

8. Waves and Optics | 波动与光学

Transverse and longitudinal waves are distinguished by vibration direction relative to propagation. The wave speed v = fλ and intensity I ∝ amplitude² hold universally. Superposition leads to interference: path difference = nλ gives constructive, (n + ½)λ gives destructive interference. Young’s double‑slit experiment yields fringe spacing Δy = λD/d; this relationship appears in both IB and AQA practical and theoretical contexts.

横波与纵波的区别在于振动方向相对于传播方向。波速 v = fλ 以及强度 I ∝ (振幅)² 普遍成立。叠加导致干涉：波程差等于 nλ 时为相长干涉，等于 (n + ½)λ 时为相消干涉。杨氏双缝实验给出条纹间距 Δy = λD/d；这一关系式出现在 IB 和 AQA 的实验与理论内容中。

v = fλ Δy = λD/d n₁ sin θ₁ = n₂ sin θ₂

Stationary (standing) waves form when two identical progressive waves travel in opposite directions; nodes and antinodes are separated by λ/4. For strings and open pipes, the fundamental frequency corresponds to λ/2 = L; for closed pipes it is λ/4 = L. Diffraction grating maxima occur at d sin θ = nλ. Total internal reflection takes place when light travels from higher to lower refractive index at an angle exceeding the critical angle θc where sin θc = n₂/n₁.

当两列相同的前进波沿相反方向传播时形成驻波；波节与波腹相距 λ/4。对于弦和开管，基频满足 λ/2 = L；闭管则为 λ/4 = L。衍射光栅的主极大满足 d sin θ = nλ。当光从高折射率介质射向低折射率介质，且入射角大于临界角 θc（sin θc = n₂/n₁）时，发生全内反射。

9. Electricity and Circuits | 电学与电路

Current I = ΔQ/Δt; potential difference V = W/Q; resistance R = V/I. Ohm’s law applies only for constant‑temperature conductors. Resistivity ρ links to resistance via R = ρL/A — a favourite experiment in both specifications. Series and parallel resistance rules must be second nature: R(series) = R₁ + R₂ + …, and 1/R(parallel) = 1/R₁ + 1/R₂ + … .

电流 I = ΔQ/Δt；电势差 V = W/Q；电阻 R = V/I。欧姆定律仅适用于恒温导体。电阻率 ρ 通过 R = ρL/A 与电阻关联——这是两大课程大纲都青睐的实验。串联和并联电阻的规则必须烂熟于心：串联 R = R₁ + R₂ + …，并联 1/R = 1/R₁ + 1/R₂ + …。

V = IR P = VI = I²R = V²/R emf ε = I(R + r)

Kirchhoff’s laws are essential for multi‑loop circuits: the junction rule (ΣI(in) = ΣI(out)) and loop rule (Σε = ΣIR). Internal resistance r causes terminal pd to drop as current increases: V = ε – Ir. Potential dividers use the ratio V(out) = V(in) × R₂/(R₁ + R₂); sensor circuits with LDRs and thermistors are a recurring theme. IB often uses these in data‑analysis tasks; AQA integrates them into practical‑based questions.

基尔霍夫定律对多回路电路至关重要：节点电流定律 (ΣI 入 = ΣI 出) 和回路电压定律 (Σε = ΣIR)。内阻 r 会使路端电压随电流增大而下降：V = ε – Ir。分压器利用关系式 V 输出 = V 输入 × R₂/(R₁ + R₂)；含光敏电阻和热敏电阻的传感器电路是反复出现的主题。IB 常在数据分析题中使用它们；AQA 则将其融入实验相关的题目中。

10. Magnetic Fields and Induction | 磁场与电磁感应

A moving charge in a magnetic field experiences force F = Bqv sin θ; for a current‑carrying wire F = BIL sin θ. Use Fleming’s left‑hand rule to determine force direction, but remember that IB also accepts the right‑hand palm rule. Charged particles spiral in uniform B‑fields; radius is r = mv/(Bq). Both mass spectrometry and cyclotrons rely on this principle.

运动电荷在磁场中受力 F = Bqv sin θ；载流导线受力 F = BIL sin θ。使用弗莱明左手定则判断受力方向，但需记住 IB 同样接受右手手掌定则。带电粒子在匀强磁场中螺旋运动；回旋半径 r = mv/(Bq)。质谱仪和回旋加速器都依赖这一原理。

F = Bqv sin θ F = BIL sin θ Φ = BA cos θ

Electromagnetic induction arises when magnetic flux Φ linked with a circuit changes. Faraday’s law gives induced emf ε = –N ΔΦ/Δt; Lenz’s law dictates the negative sign, opposing the change that produced it. Use Fleming’s right‑hand rule for directional emf (IB again allows two‑handed conventions). Generators and transformers illustrate these principles; keep step‑up and step‑down transformer relationships straight: Vₛ/Vₚ = Nₛ/Nₚ = Iₚ/Iₛ (ideal).

当穿过回路的磁通量 Φ 发生变化时产生电磁感应。法拉第定律给出感生电动势 ε = –N ΔΦ/Δt；楞次定律决定了负号，即感应效应反抗引起它的变化。使用弗莱明右手定则判断感生电动势方向（IB 同样允许双手定则）。发电机和变压器演示了这些原理；要把升压和降压变压器的关系记牢：Vₛ/Vₚ = Nₛ/Nₚ = Iₚ/Iₛ（理想情况）。

11. Thermal Physics | 热物理

Temperature is a measure of average random kinetic energy of particles; internal energy U is the sum of total random kinetic and potential energies of molecules. Specific heat capacity Q = mcΔθ and latent heat Q = mL are central to calorimetry. The mole concept and Avogadro constant connect macroscopic mass to number of particles: n = m/M = N/Nₐ.

温度是粒子平均无规动能的量度；内能 U 是分子总无规动能与势能之和。比热容 Q = mcΔθ 和潜热 Q = mL 是量热学的核心。摩尔概念和阿伏伽德罗常数将宏观质量与粒子数联系起来：n = m/M = N/Nₐ。

pV = nRT pV = ⅓ N m⟨c²⟩ Eₖ(mean) = ³⁄₂ kT

Ideal gas law pV = nRT is a necessary model; IB uses it in molecular form pV = NkT, AQA may use either. Kinetic theory links macroscopic pressure to microscopic motion: pV = ⅓ N m⟨c²⟩. This derivation leads to the average translational kinetic energy per molecule = ³⁄₂ kT, requiring you to understand significance of root‑mean‑square speed. Real gases deviate at high pressure and low temperature; interpret these in terms of finite molecular volume and intermolecular forces.

理想气体状态方程 pV = nRT 是必要的模型；IB 采用其微观形式 pV = NkT，AQA 两者皆可。分子动理论将宏观压强与微观运动联系起来：pV = ⅓ N m⟨c²⟩。由此可推导出每个分子的平均平动动能 = ³⁄₂ kT，这需要你理解均方根速率的意义。真实气体在高压和低温下会发生偏离；请从分子固有体积和分子间作用力的角度解释这些偏离。

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

The nucleus contains protons and neutrons, held by the strong force. Nuclear radius R = R₀ A¹/³ implies constant nuclear density. Radioactive decay follows N = N₀ e⁻λt, with half‑life T₁/₂ = ln2/λ. Activity A = λN is measured in becquerels. Distinguish α, β⁻, β⁺, and γ emissions; know their range and ionising ability. Beta decay involves change of quark flavour — udd → uud in β⁻, for instance. IB requires deeper quark analysis than AQA, but both cover conservation laws.

原子核包含质子和中子，由强核力束缚。核半径 R = R₀ A¹/³ 意味着核密度恒定。放射性衰变遵循 N = N₀ e⁻λt，半衰期 T₁/₂ = ln2/λ。活度 A = λN 以贝可勒尔为单位。辨别 α、β⁻、β⁺ 和 γ 辐射；了解它们的穿透距离与电离能力。β 衰变涉及夸克味的改变——例如 β⁻ 中 udd → uud。IB 的夸克分析要求比 AQA 更深，但双方均覆盖守恒定律。

N = N₀ e⁻λt E = Δm c² λ = ln2 / T₁/₂

Binding energy per nucleon explains nuclear stability; fusion and fission involve movement toward the iron‑56 peak. Mass defect Δm is converted to energy via E = Δm c²; be meticulous with atomic mass units (u) and MeV: 1 u = 931.5 MeV. In IB, the Standard Model of particles — quarks, leptons, gauge bosons and the Higgs boson — forms a substantial section; AQA includes up/down/strange quarks and interactions. Fundamental forces and their exchange particles should be committed to memory.

平均结合能解释核稳定性；聚变与裂变均朝铁‑56 峰值移动。质量亏损 Δm 通过 E = Δm c² 转化为能量；务必谨慎处理原子质量单位 (u) 与 MeV：1 u = 931.5 MeV。在 IB 中，粒子标准模型——夸克、轻子、规范玻色子和希格斯玻色子——是一个重要板块；AQA 涵盖了上/下/奇异夸克及其相互作用。基本作用力及其交换粒子需要记牢。

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IB & AQA Physics: Last-Minute Crash Revision Notes | IB AQA 物理考前冲刺笔记