📚 A-Level CCEA Physics: Last-Minute Rapid Revision Notes | CCEA A-Level 物理考前冲刺笔记
This set of condensed notes covers the essential definitions, formulas, and concepts for the CCEA A-Level Physics specification. Use them to quickly refresh your memory before the exam, focusing on key equations, experimental uncertainties, and the most frequently assessed applications across AS and A2 units.
这份精简笔记涵盖了CCEA A-Level物理考试的核心定义、公式和概念。可在考前快速回顾，重点关注关键方程、实验不确定度以及AS与A2单元中最高频的考查应用。
1. Measurements and Uncertainty | 测量与不确定度
All experimental measurements must be recorded with an absolute uncertainty, typically half the smallest scale division for a single reading, or the range/2 for repeated readings.
所有实验测量值必须记录绝对不确定度。单次读数通常取最小分度值的一半，多次读数则取（极差/2）。
Percentage uncertainty = (absolute uncertainty / measured value) × 100%. When quantities are multiplied or divided, add their percentage uncertainties.
百分比不确定度 =（绝对不确定度 / 测量值）× 100%。当物理量相乘或相除时，将各自的百分比不确定度相加。
For a quantity raised to a power n, multiply the percentage uncertainty by n. For addition or subtraction, add absolute uncertainties.
若物理量含有幂次 n，需将百分比不确定度乘以 n。进行加减运算时，则直接将绝对不确定度相加。
Precision reflects the spread of repeated measurements; accuracy indicates closeness to the true value. Use significant figures consistent with the uncertainty.
精密度反映重复测量值的分散程度；准确度表示与真值的接近程度。有效数字的位数应与不确定度匹配。
2. Motion, Forces and Energy | 运动、力与能量
The SUVAT equations apply for constant acceleration in a straight line: v = u + at ; s = ut + ½at² ; v² = u² + 2as ; s = ½(u+v)t.
匀变速直线运动的SUVAT方程适用：v = u + at ; s = ut + ½at² ; v² = u² + 2as ; s = ½(u+v)t。
Newton’s second law: net force Fₙₑₜ = ma. Weight W = mg. Always resolve forces into perpendicular components on free-body diagrams.
牛顿第二定律：净力 Fₙₑₜ = ma。重力 W = mg。务必在受力分析图中将力分解为相互垂直的分量。
Work done W = Fs cosθ, where θ is the angle between force and displacement. Kinetic energy Eₖ = ½mv². Gravitational potential energy Eₚ = mgh.
做功 W = Fs cosθ，其中 θ 为力与位移的夹角。动能 Eₖ = ½mv²。重力势能 Eₚ = mgh。
Power is the rate of doing work: P = W/t = Fv for constant velocity. Efficiency = (useful output power) / (input power) × 100%.
功率是做功的快慢：P = W/t。当速度恒定时 P = Fv。效率 =（有用输出功率）/（输入功率）× 100%。
Hooke’s law: F = kx within the elastic limit. Elastic potential energy stored in a stretched spring = ½Fx = ½kx².
胡克定律：弹性限度内 F = kx。伸长弹簧储存的弹性势能 = ½Fx = ½kx²。
3. Momentum and Circular Motion | 动量与圆周运动
Linear momentum p = mv. Impulse = FΔt = Δp. In an isolated system, total momentum is conserved in all collisions and explosions.
线动量 p = mv。冲量 = FΔt = Δp。孤立系统中，任何碰撞和爆炸的总动量始终守恒。
For elastic collisions, kinetic energy is conserved; for inelastic collisions, it is not. Use vector addition to find resultant momenta in 2D.
弹性碰撞中动能守恒，非弹性碰撞中动能不守恒。二维问题须用矢量加法求合动量。
For uniform circular motion: centripetal acceleration a = v²/r = ω²r. Centripetal force F = mv²/r = mω²r. Speed v = ωr = 2πr/T.
匀速圆周运动中：向心加速度 a = v²/r = ω²r；向心力 F = mv²/r = mω²r；线速度 v = ωr = 2πr/T。
The centripetal force is not a separate force; it is provided by tension, friction, gravity, or the normal reaction. It always points towards the centre.
向心力并非一种独立的力，由拉力、摩擦力、重力或支持力提供，方向始终指向圆心。
4. Waves, Refraction and Diffraction | 波动、折射与衍射
Wave speed v = fλ. Period T = 1/f. Phase difference in radians = (2π/λ) × path difference. Longitudinal waves oscillate parallel to propagation; transverse waves oscillate perpendicular.
波速 v = fλ。周期 T = 1/f。相位差（弧度）= (2π/λ) × 路程差。纵波振动方向与传播方向平行，横波则垂直。
Snell’s law: n₁ sinθ₁ = n₂ sinθ₂, where n = c/v. Total internal reflection occurs when the angle of incidence exceeds the critical angle c, and n₁ > n₂. sin c = n₂/n₁.
斯涅尔定律：n₁ sinθ₁ = n₂ sinθ₂，其中 n = c/v。发生全内反射的条件是入射角大于临界角 c，且 n₁ > n₂。sin c = n₂/n₁。
For a single slit of width b, the first minimum occurs at sinθ ≈ θ = λ/b. For a diffraction grating with spacing d, maxima occur at d sinθ = nλ.
单缝宽度 b 时，第一暗纹满足 sinθ ≈ θ = λ/b。光栅常数 d 的衍射光栅，亮纹满足 d sinθ = nλ。
Stationary waves on a string: distance between adjacent nodes = λ/2. In a pipe open at both ends, the fundamental frequency fits λ/2; in a pipe closed at one end, it fits λ/4.
弦上的驻波：相邻波节间距 = λ/2。两端开口管基频对应 λ/2，一端闭管基频对应 λ/4。
5. Quantum Physics and the Photoelectric Effect | 量子物理与光电效应
Photon energy E = hf = hc/λ. The electronvolt: 1 eV = 1.60 × 10⁻¹⁹ J. Energy levels are quantised; an electron dropping from E₂ to E₁ emits a photon of energy ΔE.
光子能量 E = hf = hc/λ。1 电子伏特 = 1.60 × 10⁻¹⁹ J。能级是量子化的，电子从 E₂ 跃迁至 E₁ 时释放能量为 ΔE 的光子。
Einstein’s photoelectric equation: hf = φ + Eₖₘₐₓ, where φ is the work function. The threshold frequency f₀ = φ/h. Stopping potential Vₛ = Eₖₘₐₓ/e.
爱因斯坦光电方程：hf = φ + Eₖₘₐₓ，φ 为逸出功。阈频率 f₀ = φ/h。遏止电压 Vₛ = Eₖₘₐₓ/e。
The wave model cannot explain the threshold frequency or the instantaneous emission; light must be treated as photons. Increasing intensity increases the number of photons (and thus the saturation current), not the maximum kinetic energy.
波动模型无法解释阈频率或瞬时发射，光必须视为光子。增加光强只增加光子数目（进而增大饱和电流），不提高最大动能。
Matter waves: de Broglie wavelength λ = h/p = h/mv. Electron diffraction provides evidence for the wave nature of particles.
物质波：德布罗意波长 λ = h/p = h/mv。电子衍射证实了粒子的波动性。
6. Electricity and DC Circuits | 电学与直流电路
Ohm’s law: V = IR for a conductor at constant temperature. Resistance R = ρL/A. Resistivity ρ depends on material and temperature.
欧姆定律：恒温下导体的 V = IR。电阻 R = ρL/A。电阻率 ρ 与材料及温度有关。
Series: Rₛ = R₁ + R₂ + … ; current is the same; voltages add. Parallel: 1/Rₚ = 1/R₁ + 1/R₂ + … ; voltage is the same; currents add.
串联：Rₛ = R₁ + R₂ + …；电流处处相等，总电压相加。并联：1/Rₚ = 1/R₁ + 1/R₂ + …；电压相等，总电流相加。
Power dissipated: P = IV = I²R = V²/R. E.m.f. ε = I(R + r), where r is internal resistance. Terminal p.d. V = ε – Ir.
耗散功率：P = IV = I²R = V²/R。电动势 ε = I(R + r)，r 为内阻，路端电压 V = ε – Ir。
A potential divider consists of two resistors in series: Vₒᵤₜ = (R₂/(R₁+R₂)) × Vᵢₙ. It can supply a variable voltage between 0 and Vᵢₙ.
分压器由两电阻串联组成：Vₒᵤₜ = (R₂/(R₁+R₂)) × Vᵢₙ，可提供 0 至 Vᵢₙ 之间的可变电压。
| Quantity | Series | Parallel |
| Equivalent resistance | R = R₁ + R₂ | 1/R = 1/R₁ + 1/R₂ |
| Current | I same | I = I₁ + I₂ |
| Voltage | V = V₁ + V₂ | V same |
7. Capacitors and Electric Fields | 电容器与电场
Capacitance C = Q/V, unit farad (F). For a parallel-plate capacitor, C = εA/d, where ε = ε₀εᵣ. Energy stored E = ½QV = ½CV² = Q²/(2C).
电容 C = Q/V，单位法拉（F）。平行板电容器 C = εA/d，ε = ε₀εᵣ。储存能量 E = ½QV = ½CV² = Q²/(2C)。
Charging and discharging follow exponential curves: V = V₀ e⁻ᵗ⁄ᴿᶜ, I = I₀ e⁻ᵗ⁄ᴿᶜ. Time constant τ = RC; after τ, the voltage falls to about 37% of its initial value.
充放电遵循指数曲线：V = V₀ e⁻ᵗ⁄ᴿᶜ，I = I₀ e⁻ᵗ⁄ᴿᶜ。时间常数 τ = RC；经过 τ 后，电压降至初始值约 37%。
Electric field strength E = F/q = V/d for a uniform field. Coulomb’s law for point charges: F = kQ₁Q₂/r², where k = 1/(4πε₀).
电场强度 E = F/q，匀强电场中 E = V/d。点电荷的库仑定律：F = kQ₁Q₂/r²，k = 1/(4πε₀)。
Work done moving a charge Q across a p.d. V is W = QV. Equipotential lines are perpendicular to field lines. In a radial field, E = kQ/r².
将电荷 Q 在电势差 V 间移动做功 W = QV。等势线与电场线垂直。在辐射场中 E = kQ/r²。
8. Thermal Physics and Gases | 热物理与气体
Absolute temperature T (kelvin) = θ (°C) + 273.15. The kinetic theory relates average kinetic energy to temperature: ½m〈c²〉= (3/2)kT.
绝对温度 T（开尔文）= θ（°C）+ 273.15。分子动理论将平均动能与温度联系：½m〈c²〉= (3/2)kT。
Ideal gas equation: pV = nRT, or pV = NkT. Boyle’s law (pV = constant at constant T), Charles’s law (V ∝ T at constant p) and Pressure law (p ∝ T at constant V) are special cases.
理想气体方程：pV = nRT 或 pV = NkT。玻意耳定律（恒 T 下 pV = 常数）、查理定律（恒 p 下 V ∝ T）、压强定律（恒 V 下 p ∝ T）均为其特例。
Specific heat capacity c: ΔQ = mcΔθ. Specific latent heat L: ΔQ = mL. The internal energy of an ideal gas depends only on temperature, ΔU ∝ ΔT.
比热容 c：ΔQ = mcΔθ。比潜热 L：ΔQ = mL。理想气体内能仅与温度有关，ΔU ∝ ΔT。
First law of thermodynamics: ΔU = Q + W (work done on the system is positive). For an isothermal expansion of an ideal gas, ΔU = 0 so Q = -W.
热力学第一定律：ΔU = Q + W（外界对系统做正功）。理想气体等温膨胀时 ΔU = 0，故 Q = -W。
9. Nuclear Physics and Medical Imaging | 核物理与医学成像
The nucleus is characterised by A = Z + N. Nuclear radius R = r₀A¹⁄³, where r₀ ≈ 1.2 fm. Density of nuclear matter is constant.
原子核特征参量：A = Z + N。核半径 R = r₀A¹⁄³，其中 r₀ ≈ 1.2 fm。核物质密度为常数。
Radioactive decay: Activity A = λN. Decay law N = N₀ e⁻λᵗ. Half-life T½ = ln2/λ. Mass-energy equivalence from rest energy: E = mc².
放射性衰变：活度 A = λN。衰变规律 N = N₀ e⁻λᵗ。半衰期 T½ = ln2/λ。可由质能方程得到静止能量 E = mc²。
In nuclear fission, a heavy nucleus splits into two lighter nuclei, releasing energy and neutrons. In fusion, light nuclei combine, releasing larger amounts of energy per unit mass.
核裂变中重核分裂成两个较轻核，释放能量和中子。核聚变中轻核聚合，单位质量释放的能量更大。
Ultrasound imaging uses high-frequency sound (f > 20 kHz). The acoustic impedance Z = ρc, and the intensity reflection coefficient = (Z₂ – Z₁)²/(Z₂ + Z₁)². A gel is used to match impedances.
超声成像使用高频声波（f > 20 kHz）。声阻抗 Z = ρc，强度反射系数 = (Z₂ – Z₁)²/(Z₂ + Z₁)²。使用耦合凝胶以匹配声阻抗。
In X-ray imaging, attenuation follows I = I₀ e⁻μx, where μ is the linear attenuation coefficient. Half-value thickness x½ = ln2/μ. CT scans produce 3D images using multiple X-ray projections.
X射线成像中，衰减遵循 I = I₀ e⁻μx，μ 为线性衰减系数，半值厚度 x½ = ln2/μ。CT扫描利用多个方向的X射线投影生成三维图像。
Gamma cameras detect gamma rays emitted from a radioisotope tracer. The positron emission tomography (PET) scanner detects coincidence events from electron–positron annihilation, giving functional information.
伽马相机探测放射性示踪剂发射的伽马射线。正电子发射断层扫描（PET）探测电子-正电子湮灭产生的符合事件，可提供功能信息。
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