📚 Year 13 Cambridge Physics: Core Knowledge Review | Year 13 剑桥物理：核心知识点梳理
Year 13 Cambridge Physics (A2 level) builds upon the foundations laid in Year 12, introducing deeper and more mathematically demanding concepts. This article provides a structured overview of the essential core topics, linking key ideas, equations, and practical applications that are central to the Cambridge International AS & A Level Physics (9702) syllabus. Use it as a checklist for your revision.
Year 13 剑桥物理 (A2) 在 Year 12 的基础上引入了更深层次的、数学要求更高的概念。本文系统梳理了必考的核心知识点，将关键思想、重要方程与实际应用串联起来，全面覆盖剑桥国际 AS & A Level 物理 (9702) 大纲。可用作复习自查清单。
1. Circular Motion | 圆周运动
Angular velocity ω is measured in rad s⁻¹ and relates to linear speed via v = ωr. An object moving in a circle at constant speed still accelerates because its direction changes continuously.
角速度 ω 的单位是 rad s⁻¹，与线速度的关系为 v = ωr。即使做匀速圆周运动，物体仍具有向心加速度，因为速度方向不断改变。
Centripetal acceleration a = v²/r = ω²r, always directed towards the centre. The net inward force providing this acceleration is F = m v²/r = m ω²r.
向心加速度 a = v²/r = ω²r，方向始终指向圆心。产生该加速度的合内力为 F = m v²/r = m ω²r。
2. Gravitational Fields | 引力场
Newton’s law of gravitation states F = G M m / r², where G = 6.67 × 10⁻¹¹ N m² kg⁻². Gravitational field strength g is defined as force per unit mass: g = F/m = G M / r² for a point mass or spherical body.
牛顿万有引力定律为 F = G M m / r²，G = 6.67 × 10⁻¹¹ N m² kg⁻²。引力场强度 g 定义为单位质量所受的力：对质点或球体，g = F/m = G M / r²。
Gravitational potential φ = −G M / r, with zero potential at infinity. Escape velocity vₑ = √(2 G M / r) = √(2 g r). Satellite motion obeys Kepler’s third law T² ∝ r³, derived from equating gravitational and centripetal forces.
引力势 φ = −G M / r，无穷远处为零。逃逸速度 vₑ = √(2 G M / r) = √(2 g r)。卫星运动遵循开普勒第三定律 T² ∝ r³，由引力提供向心力推导得出。
3. Temperature and Ideal Gases | 温度与理想气体
Temperature is a measure of the average random kinetic energy of particles. The thermodynamic (Kelvin) scale uses absolute zero (0 K) and triple point of water (273.16 K). T(K) = θ(°C) + 273.15.
温度是粒子平均无规则动能的量度。热力学（开尔文）温标采用绝对零度 (0 K) 和水的三相点 (273.16 K)。T(K) = θ(°C) + 273.15。
The ideal gas equation: pV = nRT = NkT, where R = 8.31 J mol⁻¹ K⁻¹, k = 1.38 × 10⁻²³ J K⁻¹. The kinetic theory model yields pV = 1/3 N m
理想气体状态方程：pV = nRT = NkT，R = 8.31 J mol⁻¹ K⁻¹，k = 1.38 × 10⁻²³ J K⁻¹。分子动理论给出 pV = 1/3 N m
4. Thermodynamics | 热力学
The first law of thermodynamics is ΔU = Q + W, where ΔU is the change in internal energy, Q is heat supplied to the system, and W is work done on the system. In the Cambridge convention, W = −p ΔV for a gas expanding at constant pressure, so ΔU = Q − p ΔV is often used.
热力学第一定律为 ΔU = Q + W，其中 ΔU 是内能变化，Q 是系统吸收的热量，W 是对系统做的功。在剑桥符号体系中，气体恒压膨胀时 W = −p ΔV，因此常写成 ΔU = Q − p ΔV。
Internal energy includes the total kinetic and potential energies of molecules. Specific heat capacity c and specific latent heat L are measured using calorimetry, e.g., electrical methods accounting for heat loss.
内能包括分子总动能和总势能。比热容 c 和比潜热 L 通过量热法测定，比如用电热法并修正热损失。
5. Simple Harmonic Motion (SHM) | 简谐运动
SHM requires a restoring force proportional to displacement: a = − ω² x. Solutions take the form x = x₀ sin(ω t) or x = x₀ cos(ω t), with v = ± ω √(x₀² − x²).
简谐运动要求回复力与位移成正比：a = − ω² x。解的形式为 x = x₀ sin(ω t) 或 x = x₀ cos(ω t)，速度 v = ± ω √(x₀² − x²)。
Energy in SHM: total energy E = ½ m ω² x₀², which is constant and continuously exchanged between kinetic and potential forms. Damping reduces amplitude; resonance occurs when driving frequency equals natural frequency ω₀.
简谐运动能量：总能量 E = ½ m ω² x₀²，保持不变且在动能与势能之间连续转换。阻尼使振幅减小；当驱动力频率等于固有频率 ω₀ 时发生共振。
6. Electric Fields | 电场
Coulomb’s law: F = (1/(4π ε₀)) Q₁ Q₂ / r², with ε₀ = 8.85 × 10⁻¹² F m⁻¹. Electric field strength E = F/q; for a point charge, E = (1/(4π ε₀)) Q / r², and for a uniform field between parallel plates, E = V / d.
库仑定律：F = (1/(4π ε₀)) Q₁ Q₂ / r²，ε₀ = 8.85 × 10⁻¹² F m⁻¹。电场强度 E = F/q；点电荷电场 E = (1/(4π ε₀)) Q / r²，平行板匀强电场 E = V / d。
Electric potential V = W/q. The potential due to a point charge is V = (1/(4π ε₀)) Q / r. Potential difference is work done per unit charge. Charged particles accelerated through a p.d. gain kinetic energy ½ m v² = q V.
电势 V = W/q。点电荷电势 V = (1/(4π ε₀)) Q / r。电势差是单位电荷移动所做的功。带电粒子经电势差加速，获得动能 ½ m v² = q V。
7. Capacitance | 电容
Capacitance C = Q / V, measured in farads (F). For a parallel-plate capacitor, C = ε₀ A / d (without dielectric). Capacitors in parallel sum C_total = C₁ + C₂, while in series 1/C_total = 1/C₁ + 1/C₂.
电容 C = Q / V，单位法拉 (F)。平行板电容器的电容 C = ε₀ A / d（无电介质）。电容并联时总电容 C_total = C₁ + C₂，串联时 1/C_total = 1/C₁ + 1/C₂。
Energy stored = ½ Q V = ½ C V² = ½ Q² / C. For a charging/discharging RC circuit, V = V₀ e^{−t/RC}, where time constant τ = RC. The current and charge change exponentially.
储存能量 = ½ Q V = ½ C V² = ½ Q² / C。在 RC 充放电电路中，V = V₀ e^{−t/RC}，时间常数 τ = RC。电流和电荷按指数规律变化。
8. Magnetic Fields | 磁场
A current-carrying conductor in a magnetic field experiences a force F = B I L sinθ, where θ is the angle between current and field. Direction is given by Fleming’s left-hand rule.
通电导线在磁场中受力 F = B I L sinθ，θ 为电流与磁场方向夹角。方向由弗莱明左手定则判断。
For a moving charge, F = B q v sinθ. If the velocity is perpendicular to a uniform B, the charge follows a circular path with radius r = m v / (B q). The Hall effect yields V_H = B I / (n q t), useful for measuring magnetic flux density or carrier density.
运动电荷受力 F = B q v sinθ。若速度垂直于匀强磁场，电荷做圆周运动，半径 r = m v / (B q)。霍尔效应给出 V_H = B I / (n q t)，可用于测量磁通密度或载流子密度。
9. Electromagnetic Induction | 电磁感应
Magnetic flux Φ = B A cosθ, and flux linkage = N Φ. Faraday’s law: induced emf ε = − d(N Φ)/dt. Lenz’s law states that the induced current opposes the change in flux that produced it.
磁通量 Φ = B A cosθ，磁链 = N Φ。法拉第定律：感应电动势 ε = − d(N Φ)/dt。楞次定律指出感应电流的磁场总是阻碍引起感应的磁通变化。
Induction explains generators (rotating coil in a magnetic field) and transformers. An ideal transformer satisfies V_s / V_p = N_s / N_p and, assuming 100% efficiency, I_p V_p = I_s V_s.
电磁感应原理可解释发电机（线圈在磁场中转动）和变压器。理想变压器满足 V_s / V_p = N_s / N_p，假设效率 100% 则有 I_p V_p = I_s V_s。
10. Alternating Currents | 交流电
An alternating voltage can be expressed as V = V₀ sin(ω t). The root-mean-square (rms) value for sinusoidal quantities is V_rms = V₀ / √2, I_rms = I₀ / √2, representing the equivalent dc heating effect.
交流电压可表示为 V = V₀ sin(ω t)。正弦量的方均根值 V_rms = V₀ / √2，I_rms = I₀ / √2，代表等效直流的热效应。
Average power in an AC circuit P = I_rms V_rms cos φ, where cos φ is the power factor. Transformers step voltage up or down; rectification (half-wave, full-wave) and smoothing with capacitors produce a steady dc output.
交流电路平均功率 P = I_rms V_rms cos φ，cos φ 为功率因数。变压器用于升降压；整流（半波、全波）和电容滤波可产生平滑的直流输出。
11. Quantum Physics | 量子物理
Photon energy E = h f = h c / λ, where h = 6.63 × 10⁻³⁴ J s. The photoelectric effect is described by h f = Φ + ½ m v²_max, demonstrating that light consists of discrete quanta and explaining the threshold frequency f₀ = Φ / h.
光子能量 E = h f = h c / λ，h = 6.63 × 10⁻³⁴ J s。光电效应方程 h f = Φ + ½ m v²_max，证实光由离散量子组成，并解释了截止频率 f₀ = Φ / h。
Wave–particle duality: electrons and other particles have a de Broglie wavelength λ = h / p, confirmed by electron diffraction. Emission and absorption line spectra provide evidence for discrete atomic energy levels, where a photon is emitted when an electron transitions between levels ΔE = h f.
波粒二象性：电子等粒子具有德布罗意波长 λ = h / p，电子衍射实验加以证实。发射和吸收线光谱为原子分立能级提供了证据，电子在能级间跃迁时放出光子，能量 ΔE = h f。
12. Nuclear Physics | 核物理
The unified atomic mass unit u = 1.66 × 10⁻²⁷ kg, equivalent to 931.5 MeV/c² via E = m c². Mass defect and binding energy explain nuclear stability; the binding energy per nucleon peaks around iron-56.
原子质量单位 u = 1.66 × 10⁻²⁷ kg，根据 E = m c² 相当于 931.5 MeV/c²。质量亏损和结合能解释了原子核的稳定性；比结合能在铁-56 附近最大。
Radioactive decay follows N = N₀ e^{−λ t}, activity A = λ N. Half-life T_{1/2} = ln 2 / λ. Fission (heavy nucleus splitting) and fusion (light nuclei combining) release energy because of the differing binding energy per nucleon. Fundamental particles and their interactions may be examined in the context of conservation laws.
放射性衰变规律 N = N₀ e^{−λ t}，活度 A = λ N。半衰期 T_{1/2} = ln 2 / λ。裂变（重核分裂）和聚变（轻核结合）因比结合能不同而释放能量。基本粒子及其相互作用可在守恒定律的背景下予以考查。
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