📚 A-Level AQA Physics: Last-Minute Revision Notes | A-Level AQA 物理：考前冲刺笔记
These concise revision notes cover the most important facts, formulas and common pitfalls across the full AQA A-Level Physics specification. Use them to quickly refresh your memory before the exam, focusing on precise definitions, key equations and the logic behind every concept. Each section pairs an English explanation with its Chinese equivalent so you can absorb the content in whichever language feels more natural under time pressure.
这份精简的考前笔记涵盖了 AQA A-Level 物理全部核心知识点、必考公式和常见易错点。考前快速浏览，重点记忆精准定义、关键方程和每个概念背后的逻辑。每个小节均采用英中对照的形式，方便你在时间紧迫的情况下用最习惯的语言吸收内容。
1. Measurements and Errors | 测量与误差
Always quote the absolute uncertainty to the same number of significant figures as the measured value. For a quantity calculated from two or more measurements, combine uncertainties using the rules: add absolute uncertainties when adding or subtracting quantities; add percentage uncertainties when multiplying or dividing.
绝对不确定度的有效数字位数必须与测量值一致。若某个量由两个或以上测量值计算得出，则需按规则合成不确定度：加减运算时相加绝对不确定度；乘除运算时相加百分比不确定度。
Systematic errors affect accuracy and can be reduced by calibrating instruments or correcting for zero error. Random errors affect precision and are reduced by taking repeat readings and calculating a mean. A result is accurate if it is close to the true value; it is precise if repeated readings show little spread.
系统误差影响准确度，可通过校准仪器或修正零点误差来减小。随机误差影响精密度，可通过多次测量取平均值来降低。若结果接近真值则准确；若多次测量结果离散很小则精密。
2. Particles and Radiation | 粒子与辐射
The strong nuclear force holds nucleons together at separations below about 0.5 fm; it is repulsive at very short range to prevent collapse. Alpha decay occurs when the nucleus is too large; a helium nucleus is emitted. Beta-minus decay changes a neutron into a proton, emitting an electron and an antineutrino.
强核力在核子间距约 0.5 fm 以内起束缚作用，极短距离时表现为排斥以防止塌缩。α 衰变发生在核过大时，释放一个氦核。β⁻ 衰变将中子转变为质子，同时放出电子和反中微子。
The photon is the exchange particle of the electromagnetic interaction. The energy of a photon is given by E = hf = hc / λ. Annihilation of a particle and its antiparticle converts their rest masses into two photons travelling in opposite directions to conserve momentum.
光子是电磁相互作用的交换粒子。光子能量 E = hf = hc / λ。正反粒子湮灭将其静质量转化为两个沿相反方向运动的光子，以遵守动量守恒。
3. Quantum Phenomena | 量子现象
The photoelectric effect shows that one electron absorbs one photon. Emission only occurs if the photon energy exceeds the work function Φ. The maximum kinetic energy of emitted electrons is Ek max = hf − Φ. The stopping potential Vs gives Ek max = eVs.
光电效应表明一个电子吸收一个光子。仅当光子能量大于功函数 Φ 时电子才能逸出。逸出电子的最大动能 Ek max = hf − Φ，遏止电势 Vs 满足 Ek max = eVs。
Electron diffraction proves wave-particle duality. The de Broglie wavelength λ = h / p. Moving electrons behave as waves; interference patterns appear when a beam passes through graphite. Threshold frequency is the minimum frequency needed for photoemission; below it, no electrons are released regardless of light intensity.
电子衍射证实了波粒二象性。德布罗意波长 λ = h / p。运动的电子表现出波动性；电子束穿过石墨会形成干涉图样。阈频率是发生光电发射所需的最低频率；低于阈频率时，无论光强多大都不会逸出电子。
4. Mechanics and Materials | 力学与材料性能
Resolve vectors into perpendicular components using trigonometry. For equilibrium, the vector sum of forces is zero and the sum of moments about any point is zero. The principle of moments: sum of clockwise moments = sum of anticlockwise moments about a pivot when balanced.
用三角函数将矢量分解为互相垂直的分量。刚体平衡条件为合外力为零，且对任意点的合力矩为零。力矩原理：平衡时，以支点为中心，顺时针力矩之和等于逆时针力矩之和。
Hooke’s law: F = kΔL within the limit of proportionality. Elastic limit: beyond this the material is permanently deformed. The Young modulus E = stress / strain = (F/A) / (ΔL/L). The area under a force-extension graph gives work done to stretch the material. Breaking stress determines when a material fractures.
在比例限度内，胡克定律 F = kΔL。弹性限度：超过此限材料发生永久形变。杨氏模量 E = 应力/应变 = (F/A) / (ΔL/L)。力−伸长图下方的面积等于拉伸材料所做的功。断裂应力决定材料何时断裂。
5. Waves and Optics | 波动与光学
Progressive waves transfer energy without net material transfer. In a standing wave, nodes have zero amplitude and antinodes have maximum amplitude; formed by superposition of two identical waves travelling in opposite directions. Path difference for constructive interference: nλ; destructive: (n + ½)λ.
行波传播能量而不伴随物质的净迁移。驻波中，波节振幅为零，波腹振幅最大；由两列完全相同、沿相反方向传播的波叠加而成。相长干涉的光程差：nλ；相消干涉：(n + ½)λ。
Refractive index n = c/v = sin i / sin r. Total internal reflection occurs when the angle of incidence exceeds the critical angle C, where sin C = 1/n. Double-slit fringe spacing w = λD / s, where D is slit-screen distance, s is slit separation. Diffraction grating: d sin θ = nλ for maxima.
折射率 n = c/v = sin i / sin r。当入射角大于临界角 C（sin C = 1/n）时发生全内反射。双缝干涉条纹间距 w = λD / s，D 为缝屏距离，s 为双缝间距。衍射光栅：亮纹条件 d sin θ = nλ。
6. Electricity and Circuits | 电流与电路
Ohm’s law: V = IR for an ohmic conductor at constant temperature. Resistivity ρ = RA / L. Superconductors have zero resistivity below a critical temperature. Power P = IV = I²R = V²/R. Internal resistance r: terminal p.d. V = ε − Ir.
欧姆定律：恒温下欧姆导体满足 V = IR。电阻率 ρ = RA / L。超导体在临界温度以下电阻率为零。功率 P = IV = I²R = V²/R。内阻 r：端电压 V = ε − Ir。
Kirchhoff’s first law: sum of currents entering a junction equals sum leaving — charge conservation. Second law: sum of e.m.f.s around a closed loop equals sum of p.d.s — energy conservation. Potential dividers use two resistors in series: Vout = Vin × R₂/(R₁ + R₂).
基尔霍夫第一定律：流入节点的电流之和等于流出电流之和——电荷守恒。第二定律：闭合回路中电动势之和等于电势差之和——能量守恒。分压器由两个串联电阻构成：Vout = Vin × R₂/(R₁ + R₂)。
7. Thermal Physics | 热物理
The internal energy U of an ideal gas is the sum of random kinetic energies of its particles. First law of thermodynamics: ΔU = Q + W, where Q is heat added to the system, W is work done on the system.
理想气体的内能 U 是其粒子无规则动能的总和。热力学第一定律：ΔU = Q + W，Q 为系统吸热，W 为外界对系统做的功。
For an ideal gas, pV = nRT = NkT. A mole contains NA = 6.02×10²³ entities. The Boltzmann constant k = R/NA. For adiabatic changes pVγ = constant where γ = Cp/Cv. In an isothermal expansion, temperature stays constant so ΔU = 0, thus Q = −W.
理想气体状态方程：pV = nRT = NkT。1 mol 包含 NA = 6.02×10²³ 个基本单元。玻尔兹曼常数 k = R/NA。绝热过程满足 pVγ = 常数，其中 γ = Cp/Cv。等温膨胀中温度不变，ΔU = 0，故 Q = −W。
8. Fields and Gravitation | 场与引力
Newton’s law of gravitation: F = G m₁m₂ / r². Gravitational field strength g = F/m = GM/r² for a radial field. Gravitational potential V = −GM/r; the potential gradient = −g. For a uniform field, g = −ΔV/Δr; lines are parallel and equally spaced.
牛顿万有引力定律：F = G m₁m₂ / r²。径向引力场强 g = F/m = GM/r²。引力势 V = −GM/r；势的梯度等于 −g。匀强场中 g = −ΔV/Δr；电场线平行且等间距。
Kepler’s third law for orbits: T² ∝ r³. Equate centripetal force mv²/r with gravitational force GMm/r² to derive v = √(GM/r) and T = 2π√(r³/GM). Energy of a satellite: total mechanical energy = −GMm/(2r) in a circular orbit.
开普勒第三定律：T² ∝ r³。令向心力 mv²/r 等于引力 GMm/r²，可推出 v = √(GM/r) 和 T = 2π√(r³/GM)。卫星圆轨道的总机械能为 −GMm/(2r)。
9. Electric Fields and Capacitance | 电场与电容
Coulomb’s law: F = (1/4πε₀) Q₁Q₂/r². Electric field strength E = F/q = (1/4πε₀) Q/r² for a point charge. Uniform field: E = V/d between parallel plates. The work done moving a charge q through a p.d. ΔV is qΔV.
库仑定律：F = (1/4πε₀) Q₁Q₂/r²。点电荷电场强度 E = F/q = (1/4πε₀) Q/r²。匀强电场：平行板间 E = V/d。移动电荷 q 经过电势差 ΔV 所做的功为 qΔV。
Capacitance C = Q/V. For a parallel plate capacitor, C = ε₀A/d with dielectric ε = εᵣ ε₀. Energy stored E = ½QV = ½CV² = ½Q²/C. In series, 1/Ctotal = 1/C₁ + 1/C₂; in parallel, Ctotal = C₁ + C₂. Exponential discharge: Q = Q₀ e−t/RC.
电容 C = Q/V。平行板电容 C = ε₀A/d，有介质时 ε = εᵣ ε₀。储能 E = ½QV = ½CV² = ½Q²/C。串联：1/C总 = 1/C₁ + 1/C₂；并联：C总 = C₁ + C₂。放电过程满足指数规律 Q = Q₀ e−t/RC。
10. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
A moving charge in a magnetic field experiences force F = BQv sin θ. Fleming’s left-hand rule gives direction. For a current-carrying conductor, F = BIL sin θ. Magnetic flux density B measured in tesla (T). Circular motion occurs when velocity is perpendicular to B: radius r = mv/(BQ).
运动电荷在磁场中受力 F = BQv sin θ。弗莱明左手定则确定方向。载流导线受力 F = BIL sin θ。磁感应强度 B 单位为特斯拉 (T)。当速度垂直于 B 时电荷做圆周运动：半径 r = mv/(BQ)。
Faraday’s law: induced e.m.f. = rate of change of magnetic flux linkage. ε = −N dΦ/dt (Lenz’s law gives the minus sign — induced current opposes the change). Flux Φ = BA cos θ; flux linkage = NΦ. A conductor moving through a field can generate e.m.f. = BLv.
法拉第定律：感应电动势 = 磁链变化率。ε = −N dΦ/dt（负号来自楞次定律——感应电流阻碍变化）。磁通量 Φ = BA cos θ；磁链 = NΦ。导体在磁场中运动可产生电动势 ε = BLv。
11. Nuclear Physics and Radioactivity | 核物理与放射性
Activity A = −dN/dt = λN measured in becquerel (Bq). Exponential decay: N = N₀ e−λt. Half-life T½ = ln 2 / λ. The radioactive decay constant λ is the probability of decay per unit time. The number of undecayed nuclei halves each half-life.
活度 A = −dN/dt = λN，单位贝克勒尔 (Bq)。衰变指数规律：N = N₀ e−λt。半衰期 T½ = ln 2 / λ。衰变常数 λ 是单位时间内的衰变概率。未衰变核的数量每经过一个半衰期减半。
Mass defect is the difference between the mass of the separated nucleons and the mass of the nucleus; it corresponds to the binding energy via ΔE = Δm c². Binding energy per nucleon peaks around iron-56. Nuclear fission of large nuclei and fusion of small nuclei both release energy.
质量亏损是分离核子总质量与原子核质量之差，通过 ΔE = Δm c² 对应结合能。比结合能在铁-56 附近最大。重核裂变与轻核聚变均释放能量。
12. Practical Skills and Data Analysis | 实验技能与数据分析
When plotting graphs, label axes with quantity and unit, use sensible scales, and plot error bars where uncertainties are known. A line of best fit should pass through as many error bars as possible. For a straight line y = mx + c, gradient m gives the relevant constant, and the y-intercept c often represents systematic offset.
作图时标明坐标轴物理量和单位，选用合理分度，并在已知不确定度时画出误差棒。最佳拟合线应穿过尽可能多的误差棒。对于直线 y = mx + c，斜率 m 给出相关常数，截距 c 常代表系统偏移。
In a required practical on resistivity, measure diameter with a micrometer for small cross-sectional area. For Young modulus, measure extension with a travelling microscope or ruler and use a long thin wire to make extension measurable. Percentage uncertainty = (absolute uncertainty / measured value) × 100%.
在测量电阻率的必做实验中，用螺旋测微器测量小截面积导线的直径。杨氏模量实验中，用游标显微镜或米尺测伸长，并选用长细金属丝使伸长可测。百分比不确定度 = (绝对不确定度 / 测量值) × 100%。
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