📚 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
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。
owards 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' 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。
ravitational 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
cale 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。
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
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
ment: 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。
², 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' harge, 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。
nit 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
parallel-plate capacitor, C = ε₀ A / d (without dielectric). Capacitors in parallel sum Ctotal = C₁ + C₂, while in series 1/Ctotal = 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 Ctotal = C₁ + C₂，串联时 1/Ctotal = 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
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。
, the charge follows a circular path with radius r = m v / (B q). The Hall effect yields VH = 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 VH = 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 Vs / Vp = Ns / Np and, assuming 100% efficiency, Ip Vp = Is Vs.
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 Vs / Vp = Ns / Np，假设效率 100% 则有 Ip Vp = Is Vs。
10. Alternating Currents | 交流电
ressed as V = V₀ sin(ω t). The root-mean-square (rms) value for sinusoidal quantities is Vrms = V₀ / √2, Irms = 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 Vrms = V₀ / √2，Irms = I₀ / √2，代表等效直流的热效应。
Average power in an AC circuit P = Irms Vrms 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 = Irms Vrms 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
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– 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
ing 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 T1/2 tting) 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 T1/2 = 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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