📚 A2 Physics: Final Review Outline | A2物理：期末复习提纲
The A2 Physics syllabus builds on AS concepts and introduces deeper theories in fields, oscillations, quantum and nuclear physics, thermal physics, and electromagnetism. This final review outline organises the core topics, key equations, and essential reasoning to help you consolidate your understanding before the exam. Use it as a checklist to identify strengths and gaps, and revisit each section with past paper questions.
A2 物理课程在 AS 基础上进一步深化，涵盖场、振动、量子与核物理、热力学以及电磁学等更深层的理论。这份期末复习提纲将核心主题、关键公式和重要推理梳理出来，帮助你在考前巩固理解。把它当作一份自查清单，找出强项与薄弱点，并结合历年真题逐一回顾每个小节。
1. Circular Motion | 圆周运动
tion is a = v²/r = rω², where v is the linear speed, ω is the angular speed (rad s⁻¹), and r is the radius.
物体以恒定速率做圆周运动时，会有一个指向圆心的向心加速度。其大小为 a = v²/r = rω²，其中 v 是线速率，ω 是角速度（单位 rad s⁻¹），r 是半径。
rω². Common examples include a car rounding a banked curve, a satellite in orbit, or a mass on a string. Remember that the centripetal force is not a new type of force but the resultant of real forces such as tension, gravity, or friction.
向心力是产生该加速度的净力：F = mv²/r = mrω²。常见例子包括汽车在倾斜弯道上行驶、轨道上的卫星或绳子末端的小球。牢记向心力并非一种新的力，而是由真实力（如拉力、重力或摩擦力）的合力提供。
F = mv²/r | a = rω² | ω = 2π/T
2. Gravitational Fields | 引力场
= F/m. For a point mass M, g = GM/r², and the force between two masses is given by Newton's law of gravitation: F = GMm/r².
引力场是质量会受到力的区域。场强 g 定义为单位质量所受的力：g = F/m。对于点质量 M，有 g = GM/r²；两个质量之间的引力由牛顿万有引力定律给出：F = GMm/r²。
Gravitational potential Vg at a point is the work done per unit mass to bring a mass from infinity to that point: Vg GM/r. The potential energy of a system is U = -GMm/r. Satellite motion, escape velocity (vesc = √2GM/r), and geostationary orbits all follow from these principles.
引力势 Vg 是指将单位质量从无穷远移到该点所做的功：Vg = -GM/r。系统的势能为 U = -GMm/r。卫星运动、逃逸速度（vesc = √2GM/r）以及地球同步轨道都源于这些原理。
g = GM/r² | Vg = -GM/r | T² ∝ r³ (Kepler's Third Law)
3. Electric Fields | 电场
harge Q, E = kQ/r² (where k = 1/(4πε₀)). The force between two point charges is given by Coulomb's law: F = kQ₁Q₂/r².
电场是电荷受到力的区域。电场强度 E 定义为单位正电荷所受的力：E = F/q。对于点电荷 Q，有 E = kQ/r²（其中 k = 1/(4πε₀)）。两点电荷之间的力由库仑定律给出：F = kQ₁Q₂/r²。
al difference and d is the plate separation. The motion of charged particles in electric fields – deflection, acceleration – is analogous to projectile motion under gravity. Electric potential Ve at a point is the work done per unit charge: Ve = kQ/r.
对于平行板间的匀强电场，E = V/d，其中 V 为电势差，d 为板间距。带电粒子在电场中的偏转和加速运动与重力场中的抛体运动类似。电场中某点的电势 Ve 定义为单位电荷的电势能：Ve = kQ/r。
E = F/q | E = V/d (uniform) | F = kQ₁Q₂/r²
4. Capacitance | 电容
per unit potential difference: C = Q/V, measured in farads (F). A parallel-plate capacitor' the relative permittivity of the dielectric, A is the plate area, and d is the separation.
电容 C 定义为单位电势差下储存的电荷量：C = Q/V，单位为法拉（F）。平行板电容器的电容公式为 C = ε₀εᵣA/d，其中 εᵣ 是介质的相对介电常数，A 为板面积，d 为间距。
/C. In RC circuits, the time constant τ = RC governs charging and discharging: V = V₀ e⁻ᵗ/ᴿᶜ for discharge. Capacitors in series combine as 1/Ctotal = Σ 1/Cᵢ, and in parallel as Ctotal = Σ Cᵢ.
电容器储存的能量为 W = ½QV = ½CV² = ½Q²/C。在 RC 电路中，时间常数 τ = RC 决定了充放电过程：放电时 V = V₀ e⁻ᵗ/ᴿᶜ。电容器串联时满足 1/C总 = Σ 1/Cᵢ，并联时 C总 = Σ Cᵢ。
C = Q/V | τ = RC | W = ½CV²
5. Magnetic Fields | 磁场
s the angle between the current direction and the field. The direction is given by Fleming's left-hand rule.
磁场对运动电荷有力的作用。一段长度为 L 的载流导体在匀强磁场 B 中所受的力为 F = BIL sinθ，其中 θ 为电流方向与磁场方向的夹角，方向由左手定则判断。
to radius r = mv/(qB). Mass spectrometers and cyclotrons rely on this principle. The Hall effect (VH rying conductor is placed in a perpendicular magnetic field, creating a transverse voltage.
对于以速度 v 运动的单个电荷 q：F = qvB sinθ。该力在磁场中提供向心力，使带电粒子做圆周运动，其半径 r = mv/(qB)。质谱仪和回旋加速器均基于此原理。当载流导体置于垂直磁场中时，会因霍尔效应产生横向电压 VH = BI/nqt。
F = BIL sinθ | r = mv/(qB) | VH = BI/nqt
6. Electromagnetic Induction | 电磁感应
When magnetic flux Φ through a circuit changes, an emf is induced. Faraday' s that the induced emf is equal to the rate of change of flux linkage: ε = -d(NΦ)/dt. Lenz's law gives the direction: the induced current opposes the change that produced it.
当穿过回路的磁通量 Φ 发生变化时，会产生感应电动势。法拉第定律指出，感应电动势等于磁链变化率的负值：ε = -d(NΦ)/dt。楞次定律给出了感应电流的方向：总是阻碍引起感应的磁通变化。
al energy to electrical energy by rotating a coil in a magnetic field; a transformer uses mutual induction to change voltages, with Vₚ/Vₛ = Nₚ/Nₛ for an ideal transformer.
对于在磁场中运动的导体，一根长度为 L、以速度 v 垂直于 B 运动的杆产生的感应电动势为 ε = BLv。发电机通过线圈在磁场中旋转将机械能转化为电能；变压器利用互感改变电压，理想变压器满足 Vₚ/Vₛ = Nₚ/Nₛ。
ε = -d(NΦ)/dt | ε = BLv | Vₚ/Vₛ = Nₚ/Nₛ
7. Alternating Currents | 交流电
root-mean-square (rms) value of an ac is the equivalent dc that delivers the same power: Irms = I₀/√2, Vrms = V₀/√2. AC circuits may contain resistors, capacitors, and inductors, each with a characteristic reactance.
交流电压按正弦规律变化：V = V₀ sin(ωt)。交流电的方均根值（rms）是产生相同功率的等效直流值：Irms = I₀/√2，Vrms = V₀/√2。交流电路可包含电阻、电容和电感，各自具有特征电抗。
Capacitive reactance XC = 1/(ωC) decreases with frequency; inductive reactance XL = ωL increases with frequency. In an LCR series circuit, the impedance Z = √(R² + (XL - XC)²) and resonance occurs when XL = XC, giving f₀ = 1/(2π√LC). Power in ac circuits is P = IrmsVrmscosφ, where cosφ is the power factor.
容抗 XC = 1/(ωC) 随频率升高而减小；感抗 XL = ωL 随频率升高而增大。在 LCR 串联电路中，阻抗 Z = √(R² + (XL - XC)²)，当 XL = XC 时发生谐振，谐振频率 f₀ = 1/(2π√LC)。交流电路中的功率为 P = IrmsVrmscosφ，其中 cosφ 为功率因数。
Irms = I₀/√2 | XC = 1/(ωC) | f₀ = 1/(2π√LC)
8. Quantum Physics | 量子物理
ght consists of photons, each with energy E = hf. The photoelectric equation is hf = Φ + Kmax, where Φ is the work function and Kmax is the maximum kinetic energy of emitted electrons.
量子物理学解释了经典物理无法解释的现象，比如光电效应。爱因斯坦提出光由光子组成，每个光子的能量为 E = hf。光电方程为 hf = Φ + Kmax，其中 Φ 是逸出功，Kmax 是发射电子的最大动能。
; transitions between levels produce line spectra, with photon energy hf = E₂ - E₁. The photoelectric experiment shows threshold frequency f₀ = Φ/h.
波粒二象性通过电子衍射得以证明：德布罗意波长 λ = h/p = h/(mv)。原子中的能级是量子化的；能级间的跃迁产生线状光谱，光子能量为 hf = E₂ - E₁。光电效应实验表明截止频率 f₀ = Φ/h。
E = hf | hf = Φ + ½mv² | λ = h/p
9. Nuclear Physics | 核物理
bility of nuclei. Nuclear reactions include alpha, beta, and gamma decay, as well as fission and fusion.
原子核由质子和中子组成，通过强核力结合在一起。质量亏损 Δm 和结合能 E = (Δm)c² 解释了原子核的稳定性。核反应包括 α、β 和 γ 衰变，以及裂变和聚变。
Radioactive decay follows the exponential law N = N₀ e⁻λt, with half-life T½ n fission, a heavy nucleus splits, releasing energy; in fusion, light nuclei combine. Mass–nergy equivalence ΔE = (Δm)c² is the key to calculating energy released in both processes.
放射性衰变遵循指数规律 N = N₀ e⁻λt，半衰期 T½ = ln2/λ。活度 A = λN。裂变中，重核分裂并释放能量；聚变中，轻核结合。质能方程 ΔE = (Δm)c² 是计算两种过程中释放能量的核心。
N = N₀ e⁻λt | T½ = ln2/λ | E = (Δm)c²
10. Thermal Physics | 热力学
+ W, where ΔU is the change in internal energy, Q is heat added to the system, and W is work done on the system.
系统的内能是其粒子无规则动能与势能之和。热力学第一定律表述为 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。
l gases obey pV = nRT. The kinetic theory relates pressure to mean square speed: pV = ⅓ Nm⟨c²⟩. The average translational kinetic energy of a molecule is ½ m⟨c²⟩ = (3/2)kT. Specific heat capacities at constant volume (CV) and constant pressure (CP) are linked by CP - CV = R for a mole.
理想气体满足 pV = nRT。分子动理论将压强与均方速率联系起来：pV = ⅓ Nm⟨c²⟩。分子的平均平动动能为 ½ m⟨c²⟩ = (3/2)kT。定容热容 CV 和定压热容 CP 对于每摩尔气体满足 CP - CV = R。
pV = nRT | ½ m⟨c²⟩ = (3/2)kT | ΔU = Q + W
11. Oscillations | 振动
o a = -ω²x. The displacement varies as x = x₀ sin(ωt) or x₀ cos(ωt), with angular frequency ω = 2πf.
当回复力与位移成正比且指向平衡位置时，物体做简谐运动：F = -kx，得出 a = -ω²x。位移按 x = x₀ sin(ωt) 或 x₀ cos(ωt) 变化，角频率 ω = 2πf。
The velocity in SHM is v = ±ω√x₀² - x², and maximum speed is vmax tant, interchanging between kinetic and potential forms. Damping reduces amplitude exponentially; forced oscillations can lead to resonance when driving frequency matches the natural frequency.
简谐运动中的速度为 v = ±ω√x₀² - x²，最大速率为 vmax = ωx₀。总能量 E = ½ mω² x₀² 保持不变，在动能与势能之间转换。阻尼使振幅指数衰减；受迫振动当驱动频率等于固有频率时发生共振。
a = -ω²x | v = ω√x₀² - x² | T = 2π√m/k
12. Waves and Polarisation | 波与偏振
ncy, and wavelength. Phase difference, superposition, and standing waves (formed by two identical waves travelling in opposite directions) are fundamental concepts.
行波传递能量而不传递物质。波动方程 v = fλ 联系了波速、频率和波长。相位差、叠加以及由两列等幅反向传播的波形成的驻波是基本概念。
tion is a property of transverse waves; only longitudinal waves cannot be polarised. Malus' r effect for sound and light shifts observed frequency when source and observer move relative to each other: f' = f (v ± vₒ)/(v ∓ vₛ) for sound.
偏振是横波的特性，纵波无法被偏振。马吕斯定律将透射光强与偏振片角度联系起来：I = I₀ cos²θ。应用包括偏振太阳镜和应力分析。声波与光波的多普勒效应指出，当波源与观察者相对运动时，观测频率会发生变化：对于声波有 f' = f (v ± vₒ)/(v ∓ vₛ)。
v = fλ | I = I₀ cos²θ | f' = f (v ± vₒ)/(v ∓ vₛ)
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