📚 A-Level AQA Physics: End-of-Term Revision Guide | A-Level AQA 物理：期末复习提纲
This comprehensive revision guide covers the core topics of the AQA A-level Physics specification, distilling key concepts, essential equations, and common pitfalls. Whether you are preparing for mock exams or consolidating your understanding before the final push, use this structured recap to focus your revision effectively.
这份全面的复习提纲涵盖了 AQA A-level 物理考试大纲的核心主题，提炼了关键概念、必备方程和常见易错点。无论你是在准备模拟考试，还是在最后冲刺前巩固理解，都可以利用这份结构化的回顾高效聚焦复习。
1. Measurements, Errors and Data Analysis | 测量、误差与数据分析
All physical quantities have a value and an associated uncertainty. Understand how to read scales, estimate random and systematic errors, and combine uncertainties in derived quantities. Precision is the spread of repeated readings, while accuracy is closeness to the true value.
所有物理量都有一个数值和相关的不确定度。要理解如何读数、估计随机误差和系统误差，并组合导出量的不确定度。精密度是重复读数的分散程度，而准确度则是与真实值的接近程度。
w reading ± half the smallest scale division; for a repeated measurement ± half the range.
绝对和相对不确定度：对于单次读数，取最小刻度的一半；对于多次重复测量，取极差的一半。
When adding or subtracting quantities, add absolute uncertainties. When multiplying or dividing, add percentage uncertainties.
加减量时，绝对不确定度相加；乘除量时，相对不确定度相加。
ine of best fit and worst fit give uncertainty in gradient and intercept. Use the formula: % uncertainty in gradient = (|best gradient – worst gradient| / best gradient) × 100%.
绘图时带上误差棒；最佳拟合线和最差拟合线给出斜率和截距的不确定度。使用公式：斜率相对不确定度 = (|最佳斜率 – 最差斜率| / 最佳斜率) × 100%。
SI base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd). Check homogeneity of equations by expressing each term in base units.
国际单位制基本单位：米(m)、千克(kg)、秒(s)、安培(A)、开尔文(K)、摩尔(mol)、坎德拉(cd)。通过将每个项以基本单位表示来检验方程的量纲一致性。
2. Particles and Radiation | 粒子与辐射
The atom consists of a nucleus containing protons and neutrons, orbited by electrons. Nuclear stability depends on the balance between the strong nuclear force and the electrostatic repulsion. Radioactive decay, antiparticles, and the photon model are central to this topic.
原子由包含质子和中子的原子核以及绕核运动的电子组成。原子核的稳定性取决于强核力与静电斥力之间的平衡。放射性衰变、反粒子和光子模型是这一主题的核心。
mass. For an electron, specific charge = 1.60×10⁻¹⁹ C / 9.11×10⁻³¹ kg ≈ 1.76×10¹¹ C kg⁻¹.
比荷 = 电荷 / 质量。电子的比荷为 1.60×10⁻¹⁹ C / 9.11×10⁻³¹ kg ≈ 1.76×10¹¹ C kg⁻¹。
n → proton + electron + antineutrino. Beta⁺ decay: proton → neutron + positron + neutrino.
α 衰变：原子核放出一个 ⁴₂He；原子序数减 2，质量数减 4。β⁻ 衰变：中子 → 质子 + 电子 + 反中微子。β⁺ 衰变：质子 → 中子 + 正电子 + 中微子。
gy E = hf = hc / λ. Planck constant h = 6.63×10⁻³⁴ J s. Electronvolt: 1 eV = 1.60×10⁻¹⁹ J.
光子能量 E = hf = hc / λ。普朗克常数 h = 6.63×10⁻³⁴ J s。电子伏特：1 eV = 1.60×10⁻¹⁹ J。
oduction: photon with sufficient energy (> 2 × rest energy of particle) creates a particle–antiparticle pair near a nucleus.
湮灭：粒子与反粒子相遇，质量转化为两个能量相等的光子 E = m c²。电子对产生：光子能量足够高（> 粒子静能量的两倍）时，在原子核附近产生粒子–反粒子对。
Fundamental forces: strong nuclear (gluons), electromagnetic (virtual photons), weak nuclear (W⁺, W⁻, Z⁰ bosons), and gravity (gravitons – not in spec).
基本相互作用：强核力（胶子）、电磁力（虚光子）、弱核力（W⁺、W⁻、Z⁰ 玻色子）和引力（引力子 – 不在考纲内）。
3. Quantum Phenomena | 量子现象
The photoelectric effect demonstrates the particle nature of light. Electromagnetic radiation arrives in discrete photons, each carrying energy hf. The work function Φ is the minimum energy needed to liberate an electron from a metal surface.
光电效应展示了光的粒子性。电磁辐射以分立的能量子到达，每个光子携带能量 hf。功函数 Φ 是将电子从金属表面释放所需的最小能量。
Einstein's photoelectric equation: Ek max = hf – Φ. Stopping potential Vs relates to maximum kinetic energy by e Vs = Ek max.
爱因斯坦光电方程：Ek max = hf – Φ。遏止电势 Vs 与最大动能的关系为 e Vs = Ek max。
Threshold frequency f0 = Φ / h. No electrons are emitted if f < f0, regardless of intensity.
截止频率 f0 = Φ / h。若入射光频率 f < f0，无论光强多大，都不会有电子发射。
on diffraction shows wave nature of particles. De Broglie wavelength λ = h / p = h / (mv).
电子衍射显示了粒子的波动性。德布罗意波长 λ = h / p = h / (mv)。
sorb or emit photons of energy exactly equal to the difference between two levels: ΔE = E₂ – on occurs when an electron moves to a higher level; ionisation is removal of the electron.
原子能级是分立的。电子吸收或放出的光子能量恰好等于两个能级之差：ΔE = E₂ – E₁。激发是指电子跃迁到较高能级；电离是指电子被完全移走。
Fluorescent tube: mercury vapour emits UV photons, which are absorbed by phosphor coating, exciting atoms that then emit visible light in de-excitation.
荧光灯管：汞蒸气发射紫外光子，被荧光粉涂层吸收，激发原子，随后在退激时发出可见光。
4. Waves and Optics | 波动与光学
wave equation v = f λ. Superposition, interference and diffraction reveal wave properties.
行波传播能量而不伴随物质的净移动。要理解横波与纵波的区别，并应用波动方程 v = f λ。叠加、干涉和衍射揭示了波动特性。
ces are coherent if they maintain a constant phase difference and have the same frequency.
相位差（Δφ）以弧度表示：Δφ = (2π × 波程差) / λ。若两个波源保持恒定的相位差且频率相同，则它们是相干的。
om slits to screen, s is slit separation. Young’s experiment supports the wave model of light.
双缝干涉：条纹间距 w = λD / s，其中 D 为双缝到屏幕的距离，s 为双缝间距。杨氏实验支持光的波动模型。
ating: d sinθ = n λ. The greater the number of slits, the sharper and brighter the maxima.
衍射光栅：d sinθ = n λ。狭缝数目越多，主极大越锐利、越明亮。
Stationary waves: formed from the superposition of two identical progressive waves travelling in opposite directions. Nodes (zero amplitude) and antinodes (maximum amplitude). At a fixed end, a node forms; at a free end, an antinode.
驻波：由两列相同的行波以相反方向叠加形成。波节（振幅为零）和波腹（振幅最大）。固定端形成波节；自由端形成波腹。
critical angle, sin C = 1 / n, for light travelling from optically denser to rarer medium.
折射：n₁ sinθ₁ = n₂ sinθ₂。当光从光密介质进入光疏介质，且入射角超过临界角时，发生全内反射，sin C = 1 / n。
5. Mechanics and Materials | 力学与材料
Newtonian mechanics governs motion and forces. Scalars have magnitude only; vectors have direction too. Free-body force diagrams and resolution of forces are essential tools. Materials respond to forces with elastic or plastic deformation, quantified by stress and strain.
牛顿力学支配着运动和力。标量只有大小；矢量还有方向。受力分析图和力的分解是基础工具。材料在受力时会发生弹性或塑性形变，由应力和应变定量描述。
for constant acceleration: v = u + a t; s = ½ (u+v) t; s = u t + ½ a t²; v² = u² + 2 a s.
匀加速运动的 SUVAT 方程：v = u + a t；s = ½ (u+v) t；s = u t + ½ a t²；v² = u² + 2 a s。
Newton's laws: 1st – an object remains at rest or uniform motion unless acted on by a resultant force; 2nd – F = m a; 3rd – e force pairs. Momentum p = m v; rate of change of momentum relates to force: F = Δp / Δt.
牛顿定律：第一定律 – 物体保持静止或匀速直线运动，除非受到合力作用；第二定律 – F = m a；第三定律 – 作用力与反作用力等大反向。动量 p = m v；动量变化率与力相关：F = Δp / Δt。
xternal resultant force. Elastic collisions conserve kinetic energy; inelastic collisions do not.
动量守恒定律：若系统不受外合力，碰撞前后总动量保持不变。弹性碰撞动能守恒；非弹性碰撞动能不守恒。
ensionless). Young modulus E = σ / ε. The limit of proportionality is where Hooke’s law (σ ∝ ε) ends.
应力 σ = F / A（单位 Pa）；应变 ε = ΔL / L（无量纲）。杨氏模量 E = σ / ε。比例极限是胡克定律（σ ∝ ε）终止的位置。
Force– tensile stress, fracture. Energy stored under elastic region = area under graph = ½ F ΔL.
韧性材料的力–伸长量曲线：初始线性区（弹性段）、弹性极限、屈服点、塑性流动、颈缩、抗拉强度、断裂。弹性区储存的能量 = 图线下面积 = ½ F ΔL。
6. Electricity | 电学
Electric circuits transfer energy from a source to components. Current is the rate of flow of charge, potential difference is the work done per unit charge, and resistance opposes current. Kirchhoff’s laws and potential divider circuits are fundamental analysis tools.
电路将能量从电源传递到各个元件。电流是电荷流动的速率，电势差是每单位电荷所做的功，电阻阻碍电流。基尔霍夫定律和分压电路是基本的分析工具。
Ohm’s law: for a metallic conductor at constant temperature, V ∝ tance R = V / I. Resistivity ρ = R A / L. Resistivity depends on material and temperature.
欧姆定律：对于恒温下的金属导体，V ∝ I。电阻 R = V / I。电阻率 ρ = R A / L。电阻率取决于材料和温度。
to a junction = Σ I out. Second law: in a closed loop, Σ emf = Σ IR (energy conservation).
基尔霍夫第一定律：流入节点的电流之和等于流出该节点的电流之和。第二定律：在一个闭合回路中，总电动势等于各元件电压降之和（能量守恒）。
Potential divider: Vout = Vin × (R₂ / (R₁ + R₂)). A variable resistor or sensor (thermistor, LDR) can alter Vout.
分压器：Vout = Vin × (R₂ / (R₁ + R₂))。可变电阻或传感器（热敏电阻、光敏电阻）可以改变 Vout。
Internal resistance r of a cell: terminal p.d. V = ε – I r. ε = I (R + r). Maximum power delivered to a load when R = r.
电源内阻 r：路端电压 V = ε – I r。ε = I (R + r)。当负载电阻等于内阻时，输出功率最大。
rgy transferred W = I V t. The kilowatt-hour (kWh) is a unit of energy, 1 kWh = 3.6×10⁶ J.
功率 P = V I = I² R = V² / R。转移的能量 W = I V t。千瓦时（kWh）是能量单位，1 kWh = 3.6×10⁶ J。
7. Circular Motion | 圆周运动
An object moving in a circle at constant speed has changing velocity because its direction changes continuously. The net inward force, the centripetal force, produces a centripetal acceleration towards the centre.
做匀速圆周运动的物体，速度大小不变但方向持续改变，因此速度矢量在变化。指向圆心的净力，即向心力，产生向心加速度。
Angular speed ω = Δθ / Δt = 2πf = 2π / T. Linear speed v = ω r.
角速度 ω = Δθ / Δt = 2πf = 2π / T。线速度 v = ω r。
Centripetal acceleration a = v² / r = ω² r. Centripetal force F = m a = m v² / r = m ω² r.
向心加速度 a = v² / r = ω² r。向心力 F = m a = m v² / r = m ω² r。
Examples: tension in a string for a whirling stone; friction for a car rounding a bend; gravitational attraction for satellites; electric force for electron orbiting a nucleus (Bohr model).
实例：旋转石头的绳中张力；过弯汽车所受的摩擦力；卫星所受的万有引力；电子绕核运动的库仑力（玻尔模型）。
8. Simple Harmonic Motion (SHM) | 简谐运动
SHM occurs when the restoring force (or acceleration) is directly proportional to displacement from equilibrium and always directed towards equilibrium: a ∝ – x. The solutions are sinusoidal in time.
简谐运动发生在恢复力（或加速度）与离开平衡位置的位移成正比，且总是指向平衡位置时：a ∝ – x。解是时间的正弦函数。
Defining equation: a = – ω² x. ω = 2πf. Maximum acceleration amax = ω² A, where A is amplitude.
定义方程：a = – ω² x。ω = 2πf。最大加速度 amax = ω² A，其中 A 为振幅。
Displacement: x = A sin(ω t) or x = A cos(ω t). Velocity: v = ± ω √A² – x². Maximum speed vmax = ω A at x = 0.
位移：x = A sin(ω t) 或 x = A cos(ω t)。速度：v = ± ω √A² – x²。最大速率 vmax = ω A 发生在 x = 0 处。
Mass–spring system: T = 2π √m / k. Simple pendulum (small angles): T = 2π √L / g. Check that these are independent of amplitude for SHM.
弹簧振子：T = 2π √m / k。单摆（小角度）：T = 2π √L / g。验证这些周期与振幅无关，符合简谐运动特征。
al energy E = ½ m ω² A² = constant. Kinetic and potential energies interchange. For a mass–spring system, E = ½ k A².
简谐运动中的能量：总能量 E = ½ m ω² A² = 常数。动能与势能相互转化。对于弹簧振子，E = ½ k A²。
Damping: light damping gives a slightly reduced amplitude over many oscillations; heavy damping returns to equilibrium without oscillating; critical damping gives the fastest return to equilibrium without oscillating. Resonance occurs when driving frequency equals the natural frequency, giving maximum amplitude.
阻尼：轻阻尼使振幅在多周期中逐渐减小；重阻尼不震荡直接返回平衡；临界阻尼是在不震荡的情况下最快返回平衡。当驱动频率等于固有频率时发生共振，振幅达到最大。
9. Thermal Physics | 热物理
The kinetic theory of gases links macroscopic properties (pressure, volume, temperature) to microscopic molecular motion. Internal energy is the sum of the random kinetic energies and potential energies of particles. The First Law of Thermodynamics governs energy transfers.
气体动理论将宏观性质（压强、体积、温度）与微观分子运动联系起来。内能是粒子随机动能和势能的总和。热力学第一定律支配着能量的传递。
Absolute temperature T (in kelvin) is proportional to average random kinetic energy of particles: ⟨Ek⟩ = (3/2) k T for a monatomic gas, where k = 1.38×10⁻²³ J K⁻¹.
绝对温度 T（单位开尔文）与粒子的平均随机动能成正比：对于单原子气体，⟨Ek⟩ = (3/2) k T，k = 1.38×10⁻²³ J K⁻¹。
p V = n R T, with R = 8.31 J mol⁻¹ K⁻¹. Also p V = N k T, where N is number of molecules.
理想气体状态方程：p V = n R T，R = 8.31 J mol⁻¹ K⁻¹。也可写为 p V = N k T，N 为分子数。
Kinetic theory model assumptions: large number of identical molecules in random, rapid motion; volume of molecules negligible compared to container; all collisions are perfectly elastic and duration of collisions negligible; no intermolecular forces except during collisions.
动理论模型假设：大量相同分子做快速、无规则运动；分子自身体积相对容器可忽略；所有碰撞完全弹性，碰撞持续时间可忽略；除碰撞瞬间外，分子间无作用力。
= Q + W, where ΔU is change in internal energy, Q is heat added to system, W is work done on efine with signs consistently). Work done by gas expanding at constant pressure: W = p ΔV.
第一定律：ΔU = Q + W，ΔU 为内能变化，Q 为加入系统的热量，W 为对系统做的功（需统一符号）。恒压膨胀气体对外做功：W = p ΔV。
nge, temperature stays constant while energy goes into breaking bonds (potential energy change).
比热容 c = ΔE / (m Δθ)。潜热 L = Q / m。在相变过程中，温度保持不变，而能量用于打破分子键（势能变化）。
10. Gravitational and Electric Fields | 引力场和电场
Fields represent non-contact forces. Both gravitational and electric fields follow inverse-square laws for point sources and are radial. Field strength, potential and potential energy are key parallel concepts. Comparison helps deepen understanding.
场代表非接触力。引力场和电场都遵循点源的平方反比定律，且是辐射状的。场强、势和势能是关键的平行概念。对比有助于加深理解。
Newton' strength g = F / m = G M / r² (radial). For a uniform field, g = constant (e.g. near Earth's surface).
牛顿万有引力定律：F = G M m / r²，G = 6.67×10⁻¹¹ N m² kg⁻²。引力场强 g = F / m = G M / r²（辐射状）。对于匀强场，g = 常数（如地球表面附近）。
Coulomb' th E = F / q = Q / (4 π ε₀ r²) (radial). Uniform field between parallel plates: E = V / d.
库仑定律：F = (1 / (4 π ε₀)) Q q / r²，ε₀ = 8.85×10⁻¹² F m⁻¹。电场强度 E = F / q = Q / (4 π ε₀ r²)（辐射状）。平行板间的匀强电场：E = V / d。
Gravitational potential Vg = – G M / r, at infinity zero. Electric potential Ve / (4 π ε₀ r), with sign of Q. Work done in moving a mass/charge between points: ΔW = m ΔVg or ΔW = q ΔVe.
引力势 Vg = – G M / r，无穷远为零。电势 Ve = Q / (4 π ε₀ r)，符号由 Q 决定。移动质量或电荷所做的功：ΔW = m ΔVg 或 ΔW = q ΔVe。
Equipotential surfaces are perpendicular to field lines. For a point charge, they are concentric spheres. No work is done moving along an equipotential.
等势面与电场线垂直。对于点电荷，等势面是同心球面。沿等势面移动不做功。
r orbit, gravitational force provides centripetal force: G M m / r² = m v² / r. Derive v = √G M / r, T² ∝ r³ (Kepler's third law). Total energy of a satellite = – G M m / (2 r).
卫星运动：对于圆形轨道，万有引力提供向心力：G M m / r² = m v² / r。推导得 v = √G M / r，T² ∝ r³（开普勒第三定律）。卫星的总能量 = – G M m / (2 r)。
11. Capacitors and Electromagnetic Induction | 电容器与电磁感应
Capacitors store energy in an electric field. The time-dependent charging and discharging through a resistor is exponential. Electromagnetic induction links changing magnetic flux to induced e.m.f., underpinning generators and transformers.
电容器利用电场储存能量。通过电阻的充放电过程呈指数变化。电磁感应将变化的磁通量与感应电动势联系起来，是发电机和变压器的基础。
C V² = ½ Q² / C. For a parallel plate, C = ε₀ A / d (dielectric constant κ multiplies ε₀).
电容 C = Q / V，单位法拉(F)。储存能量 E = ½ Q V = ½ C V² = ½ Q² / C。平行板电容器 C = ε₀ A / d（若加介质，κ 乘 ε₀）。
Charging: Q = Q₀ (1 – e-t / RC), V = V₀ (1 – e-t / RC). Discharging: Q = Q₀ e-t / RC, V = V₀ e-t / RC. Time constant τ = R C; time to fall to 37% of initial value.
充电：Q = Q₀ (1 – e-t / RC)，V = V₀ (1 – e-t / RC)。放电：Q = Q₀ e-t / RC，V = V₀ e-t / RC。时间常数 τ = R C；即衰减到初始值 37% 所需的时间。
Magnetic flux Φ = B A cosθ. Flux linkage NΦ. Faraday’s law: induced e.m.f. ε = – the direction of induced e.m.f. opposes the change causing it, indicated by negative sign.
磁通量 Φ = B A cosθ。磁通链 NΦ。法拉第定律：感应电动势 ε = – N (ΔΦ / Δt)。楞次定律：感应电动势的方向总是阻碍引起它的变化，即公式中的负号。
orm magnetic field gives sinusoidal e.m.f. ε = B A N ω sin(ω t). Peak e.m.f. ε₀ = B A N ω.
交流电产生：线圈在匀强磁场中匀速转动，产生正弦电动势 ε = B A N ω sin(ω t)。峰值电动势 ε₀ = B A N ω。
Transformers: Vs / Vp = Ns / Np. For an ideal transformer, power input = power output: Ip Vp = Is Vs. Efficiency = (Is Vs / Ip Vp) × 100%. Eddy currents are reduced using laminated iron cores.
变压器：Vs / Vp = Ns / Np。理想变压器输入功率等于输出功率：Ip Vp = Is Vs。效率 = (Is Vs / Ip Vp) × 100%。使用叠片式铁芯可减少涡流。
12. Nuclear Physics and Radioactivity | 核物理与放射性
Nuclear processes release enormous energies, governed by mass–energy equivalence. The stability of nuclei is described by the binding energy per nucleon curve. Radioactive decay follows a statistical exponential law.
核过程释放巨大能量，由质能等价关系决定。原子核的稳定性用比结合能曲线描述。放射性衰变遵循统计性的指数规律。
Mass defect Δm = (Z mp + N mn) – mnucleus. Binding energy Eb = Δm c². 1 u = 931.5 MeV. Binding energy per nucleon peaks at iron-56.
质量亏损 Δm = (Z mp + N mn) – 原子核质量。结合能 Eb = Δm c²。1 u = 931.5 MeV。比结合能在铁-56 处达到峰值。
Nuclear fission: a large nucleus (e.g. U-235) splits into two smaller nuclei plus neutrons, releasing energy. Nuclear fusion: two light nuclei join to form a heavier nucleus, releasing energy (e.g. proton–proton chain in stars).
核裂变：重核（如铀-235）分裂成两个较小的核并释放中子和能量。核聚变：两个轻核结合成较重的核并释放能量（例如恒星中的质子-质子链反应）。
Radioactive decay: activity A = λ N, where λ is decay constant. Decay law: N = N₀ e-λ t. Half-life T₁/₂ = ln 2 / λ. The activity also halves each half-life.
放射性衰变：活度 A = λ N，λ 为衰变常数。衰变规律：N = N₀ e-λ t。半衰期 T₁/₂ = ln 2 / λ。每经过一个半衰期，活度减半。
Exponential decay curve and use of log graphs: plotting ln N or ln A against t gives a straight line with gradient –λ.
指数衰变曲线及对数图应用：以 ln N 或 ln A 对 t 作图，得到一条斜
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