📚 Year 13 WJEC Physics Core Knowledge Review | Year 13 WJEC 物理核心知识点梳理
This article provides a comprehensive review of the core topics covered in Year 13 WJEC Physics, including oscillations, thermodynamics, nuclear physics, and field theory. It is designed to help students consolidate their understanding and prepare effectively for the A2 examinations.
本文全面梳理 Year 13 WJEC 物理的核心主题，涵盖简谐运动、热力学、原子核物理以及场论等内容，旨在帮助学生巩固理解并高效备考 A2 考试。
1. Simple Harmonic Motion (SHM) | 简谐运动
Simple harmonic motion occurs when the acceleration of an object is directly proportional to its displacement from equilibrium and always directed towards that equilibrium position. The defining equation is a = -ω²x, where ω is the angular frequency.
当物体的加速度与其离开平衡位置的位移成正比且始终指向平衡位置时，物体做简谐运动。定义方程为 a = -ω²x，其中 ω 为角频率。
The period T of oscillation is independent of amplitude for a given system and is related to angular frequency by T = 2π/ω. For a mass-spring system, T = 2π√(m/k).
对于确定的系统，振荡周期 T 与振幅无关，且满足 T = 2π/ω。对于弹簧振子，T = 2π√(m/k)。
Etotal = ½ m ω² A² = ½ k A²
The total energy in undamped SHM remains constant, alternating between kinetic and potential forms. Kinetic energy is maximum at equilibrium, while potential energy is maximum at the extremes.
无阻尼简谐运动的总能量保持不变，在动能和势能之间交替转化。动能于平衡位置最大，势能在位移最大处最大。
2. Damping and Resonance | 阻尼与共振
Damping causes the amplitude of an oscillator to decrease over time due to energy dissipation. Light damping results in a gradual decay, while critical damping brings the system to equilibrium in the shortest time without oscillating. Overdamping produces a slower return to equilibrium.
阻尼使振荡器的振幅随时间减小，原因在于能量耗散。轻阻尼产生缓慢衰减；临界阻尼使系统在最短时间内回到平衡位置且不振荡；过阻尼则使恢复过程更慢。
Resonance occurs when an oscillator is driven at its natural frequency, causing a large increase in amplitude. At resonance, the driving frequency matches the natural frequency, and energy transfer is most efficient. The sharpness of the resonance peak is described by the quality factor Q.
当驱动频率等于振子的固有频率时发生共振，振幅大幅增加。共振时能量传输效率最高，共振峰的尖锐程度用品质因数 Q 描述。
- Natural frequency f₀ = 1/(2π) √(k/m) for mass-spring.
- Damping reduces the amplitude at resonance and broadens the peak.
弹簧振子的固有频率 f₀ = 1/(2π) √(k/m)；阻尼会降低共振振幅并使峰变宽。
3. Kinetic Theory and Ideal Gases | 分子动理论与理想气体
The kinetic theory models a gas as a large number of tiny particles in random motion. The pressure exerted by an ideal gas results from collisions with the container walls and is given by p = (1/3)(N/V) m ⟨c²⟩, where ⟨c²⟩ is the mean square speed.
分子动理论将气体视为大量微小粒子做无规则运动。理想气体的压强源于粒子与容器壁的碰撞，表示为 p = (1/3)(N/V) m ⟨c²⟩，其中 ⟨c²⟩ 为均方速率。
The ideal gas equation relates the macroscopic variables: pV = nRT = NkBT, where n is the number of moles and N is the number of molecules. It holds for low pressure and high temperature.
理想气体状态方程联系宏观量：pV = nRT = NkBT，n 为摩尔数，N 为分子数。该方程适用于低气压和高温条件。
½ m ⟨c²⟩ = (3/2) kBT
The average translational kinetic energy of a molecule is directly proportional to the absolute temperature T. This links the microscopic kinetic energy to the macroscopic temperature.
分子平均平动动能与绝对温度 T 成正比，将微观动能与宏观温度联系起来。
4. First Law of Thermodynamics | 热力学第一定律
The first law states that the change in internal energy ΔU of a system equals the heat added Q minus the work done by the system W: ΔU = Q – W. Alternatively, if work is done on the system, ΔU = Q + W.
热力学第一定律指出，系统内能的增量 ΔU 等于吸收的热量 Q 减去系统对外做的功 W：ΔU = Q – W。若外界对系统做功，则 ΔU = Q + W。
For an ideal gas, internal energy depends only on temperature. In an isothermal process, ΔU = 0 and Q = W. In an adiabatic process, Q = 0, so ΔU = -W, and the gas follows pVγ = constant, where γ = Cp/Cv.
对于理想气体，内能仅取决于温度。等温过程中 ΔU = 0，Q = W；绝热过程中 Q = 0，ΔU = -W，气体满足 pVγ = 常数，其中 γ = Cp/Cv。
| Isothermal (T constant) | ΔU = 0, Q = W, pV = constant |
| Adiabatic (Q = 0) | ΔU = -W, pVγ = constant, TVγ-1 = constant |
等温过程：ΔU = 0, Q = W, pV = 常数；绝热过程：Q = 0, ΔU = -W, pVγ = 常数，且 TVγ-1 = 常数。
5. Radioactive Decay and Half-life | 放射性衰变与半衰期
Radioactive decay is a random and spontaneous process in which an unstable nucleus emits radiation. The activity A is the number of decays per second, measured in becquerels (Bq).
放射性衰变是一种随机且自发的物理过程，不稳定的原子核会发射辐射。活度 A 是每秒衰变次数，单位为贝克勒尔 (Bq)。
A = λN, N = N₀ e-λt, T1/2 = ln 2 / λ
The decay law N = N₀ e-λt gives the number of undecayed nuclei after time t. The half-life T1/2 is the time taken for half the nuclei to decay, independent of the initial number.
衰变定律 N = N₀ e-λt 表示经过时间 t 后的未衰变原子核数。半衰期 T1/2 是半数核子发生衰变所需的时间，与初始核子数无关。
Background radiation must be subtracted from measured count rates. Decay can be represented by exponential graphs, and the decay constant λ is the probability of decay per unit time.
测量计数率时需扣除本底辐射。衰变可用指数曲线表示，衰变常量 λ 是单位时间内每个原子核的衰变概率。
6. Nuclear Fission and Fusion | 核裂变与核聚变
Nuclear fission involves splitting a heavy nucleus (e.g. uranium-235) into two smaller nuclei, releasing energy and several neutrons. A chain reaction can be sustained if at least one neutron triggers further fission.
核裂变是将重核（如铀-235）分裂成两个较轻的原子核，释放能量和若干个中子。若至少有一个中子继续引发裂变，则可持续链式反应。
Nuclear fusion combines light nuclei (e.g. deuterium and tritium) to form a heavier nucleus, releasing far more energy per unit mass than fission. High temperatures are required to overcome electrostatic repulsion.
核聚变将轻核（如氘和氚）结合成较重的原子核，单位质量释放的能量远高于裂变。需要极高温度以克服库仑排斥力。
In fission reactors, control rods absorb neutrons to regulate the reaction, and moderators slow down neutrons to increase the probability of fission. Energy released is calculated from mass defect using E = Δmc².
在裂变反应堆中，控制棒吸收中子以调节反应速率；慢化剂使中子减速以增大裂变概率。释放的能量通过质量亏损按 E = Δmc² 计算。
7. Gravitational Fields | 引力场
A gravitational field is a region where a mass experiences a force. Field strength g is defined as force per unit mass: g = F/m (N kg⁻¹). For a point mass or outside a sphere, g = GM/r².
引力场是质量受到引力的区域，场强 g 定义为单位质量所受的力，g = F/m (N kg⁻¹)。对于点质量或球体外区域，g = GM/r²。
Gravitational potential V is the work done per unit mass to bring a test mass from infinity to a point: V = -GM/r. The potential energy of two masses is U = -GMm/r.
引力势 V 是把单位质量从无限远移动到某点所做的功：V = -GM/r。两个质量之间的引力势能为 U = -GMm/r。
Kepler’s laws and satellite motion derive from Newton’s law of gravitation. Geostationary satellites orbit with a period of 24 hours directly above the equator.
开普勒定律和卫星运动均可通过牛顿引力定律推导。地球同步卫星周期为 24 小时，位于赤道正上方。
8. Electric Fields | 电场
An electric field surrounds a charged object and exerts force on other charges. Electric field strength E is force per unit positive charge: E = F/q (N C⁻¹). For a point charge, E = kQ/r² = Q/(4πε₀r²).
电场包围带电物体并对其它电荷施加力。电场强度 E 定义为每单位正电荷所受的力：E = F/q (N C⁻¹)。对于点电荷，E = kQ/r² = Q/(4πε₀r²)。
Electric potential V at a point is the work done per unit charge to move a positive test charge from infinity to that point: V = kQ/r. The potential difference ΔV between two points is the work per unit charge.
电势 V 是将单位正电荷从无限远移到某点所做的功：V = kQ/r。两点之间的电势差 ΔV 是移动单位电荷所做的功。
Between parallel plates, the field is uniform: E = ΔV/d. A charge moving between plates gains kinetic energy equal to qΔV, leading to the electronvolt unit: 1 eV = 1.6 × 10⁻¹⁹ J.
在平行板之间电场均匀：E = ΔV/d。电荷在板间运动获得动能 qΔV，据此定义电子伏特：1 eV = 1.6 × 10⁻¹⁹ J。
9. Capacitance | 电容
Capacitance C is the charge stored per unit potential difference: C = Q/V, measured in farads (F). The energy stored in a capacitor is E = ½ QV = ½ CV² = ½ Q²/C.
电容 C 是储存电荷与电势差的比值：C = Q/V，单位为法拉 (F)。电容器储存的能量为 E = ½ QV = ½ CV² = ½ Q²/C。
During charging of a capacitor through a resistor, the voltage follows V = V₀(1 – e-t/RC). The time constant τ = RC determines how quickly the capacitor charges or discharges; after one time constant, voltage reaches ~63% of maximum.
电容器通过电阻充电时，电压满足 V = V₀(1 – e-t/RC)。时间常数 τ = RC 决定充放电的快慢；经过一个时间常数，电压达到最大值的约 63%。
Discharge follows Q = Q₀ e-t/RC. The half-life of discharge is T1/2 = RC ln 2. Exponential decay graphs and logarithmic plots can be used to determine RC.
放电过程满足 Q = Q₀ e-t/RC，放电半衰期为 T1/2 = RC ln 2。利用指数衰减图和线性对数图可求出 RC 时间常数。
10. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
A magnetic field exerts a force on a moving charge: F = BQv sinθ, and on a current-carrying conductor of length L: F = BIL sinθ. The direction is given by Fleming’s left-hand rule.
磁场对运动电荷的作用力为 F = BQv sinθ，对长度为 L 的载流导线的作用力为 F = BIL sinθ。方向由弗莱明左手定则确定。
Magnetic flux Φ = BA cosθ, measured in webers (Wb). Faraday’s law states that the induced emf equals the negative rate of change of flux linkage: ε = -d(NΦ)/dt. Lenz’s law gives the direction of the induced current to oppose the change causing it.
磁通量 Φ = BA cosθ，单位为韦伯 (Wb)。法拉第电磁感应定律指出，感应电动势等于磁链变化率的负值：ε = -d(NΦ)/dt。楞次定律给出感应电流方向，总是阻碍引起感应的磁通变化。
For a conductor of length L moving perpendicularly through a field with velocity v, ε = BLv. Transformers operate on mutual induction, and the turns ratio determines voltage step-up or step-down: Vs/Vp = Ns/Np.
长度为 L 的导线在磁场中以速度 v 垂直切割磁感线时，ε = BLv。变压器基于互感原理工作，匝数比决定升压或降压：Vs/Vp = Ns/Np。
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