📚 Year 13 WJEC Physics: Formula & Theorem Quick-Reference Handbook | Year 13 WJEC 物理：公式定理速查手册
This quick-reference handbook compiles all the essential formulae, theorems, and key relationships required for the Year 13 WJEC Physics specification. Use it to reinforce your understanding, check derivations, and memorise the core equations for examinations. Each section is paired with concise explanations in both English and Chinese to support bilingual learning.
本速查手册整理了Year 13 WJEC物理考试所必需的所有核心公式、定理和关键关系。你可以用它来巩固理解、核对推导过程并记忆考试核心方程。每个小节都配有简洁的英中双语解释，助力双语学习。
1. Circular Motion & Centripetal Force | 圆周运动与向心力
= ωr. The centripetal acceleration is a = v²/r = ω²r, always directed towards the centre.
对于以半径 r 和角速度 ω 做匀速圆周运动的物体，线速度 v 由 v = ωr 给出。向心加速度 a = v²/r = ω²r，方向始终指向圆心。
v = ωr a = v²/r = ω²r F = mv²/r = mω²r
e centre: F = mv²/r = mω²r. The period T is the time for one revolution: T = 2π/ω = 2πr/v.
向心力 F 是指向圆心的合力：F = mv²/r = mω²r。周期 T 为旋转一圈的时间：T = 2π/ω = 2πr/v。
- Angular speed ω = 2πf, where f is frequency in hertz.
- 角速度 ω = 2πf，其中 f 是以赫兹为单位的频率。
2. Simple Harmonic Motion (SHM) | 简谐运动
quation is a = -ω²x, where a is acceleration, x displacement, and ω the angular frequency.
简谐运动发生在恢复力与位移成正比且方向相反时。定义方程为 a = -ω²x，其中 a 是加速度，x 是位移，ω 是角频率。
a = -ω²x x = A cos(ωt + φ) v = ± ω √A² - x²
ₐₓ = ωA occurs at equilibrium; the maximum acceleration aₘₐₓ = ω²A occurs at the extremes.
位移随时间的变化为 x = A cos(ωt + φ) 或 x = A sin(ωt + φ)。最大速度 vₘₐₓ = ωA 发生在平衡位置；最大加速度 aₘₐₓ = ω²A 发生在端点。
- Period T = 2π/ω, frequency f = 1/T.
- 周期 T = 2π/ω，频率 f = 1/T。
- For a mass-spring system: T = 2π√m/k; for a simple pendulum: T = 2π√L/g.
- 弹簧振子：T = 2π√m/k；单摆：T = 2π√L/g。
3. Gravitational Fields | 引力场
Newton' th g is the force per unit mass: g = F/m = -GM/r². The negative sign indicates attraction.
牛顿万有引力定律：F = -GMm/r²。引力场强度 g 是单位质量所受的力：g = F/m = -GM/r²。负号表示吸引力。
F = -GMm/r² g = -GM/r² V = -GM/r
it mass to bring a mass from infinity: V = -GM/r. The potential energy is U = mV = -GMm/r.
引力势 V 是将单位质量从无穷远处移动到该点所做的功：V = -GM/r。势能为 U = mV = -GMm/r。
- Escape velocity vₑₛc = √2GM/R.
- 逃逸速度 vₑₛc = √2GM/R。
- Kepler's Third Law: T² ∝ r³ (for circular orbits).
- 开普勒第三定律：T² ∝ r³（适用于圆轨道）。
4. Thermal Physics & Ideal Gases | 热物理与理想气体
as constant. Alternatively, pV = NkT, with N being the number of molecules and k Boltzmann's constant.
理想气体状态方程将压强 p、体积 V、温度 T 和物质的量 n 联系起来：pV = nRT，其中 R 是摩尔气体常数。亦可写作 pV = NkT，N 为分子数，k 为玻尔兹曼常数。
pV = nRT pV = NkT k = R / Nₐ
The kinetic theory model gives the average translational kinetic energy of a molecule: ½ m〈c²〉 = ³/₂ kT. The pressure is p = ⅓ ρ〈c²〉, where ρ is density.
分子动理论模型给出分子的平均平动动能：½ m〈c²〉 = ³/₂ kT。压强为 p = ⅓ ρ〈c²〉，其中 ρ 是密度。
- First law of thermodynamics: ΔU = Q + W (where W is work done on the system).
- 热力学第一定律：ΔU = Q + W（W 为对系统做的功）。
5. Electric Fields & Coulomb's Law | 电场与库仑定律
Coulomb' k = 1/(4πε₀). The electric field strength E is the force per unit charge: E = F/q = kQ/r².
点电荷库仑定律：F = kQ₁Q₂/r²，其中 k = 1/(4πε₀)。电场强度 E 是单位电荷所受的力：E = F/q = kQ/r²。
F = kQ₁Q₂/r² E = F/q = kQ/r² V = kQ/r
to a point charge is V = kQ/r. The relationship between field and potential is E = -dV/dr.
点电荷的电势 V 为 V = kQ/r。场与势的关系为 E = -dV/dr。
- Uniform field: E = V/d (parallel plates).
- 匀强电场：E = V/d（平行板）。
- Force on a charge in uniform field: F = qE.
- 电荷在匀强电场中的受力：F = qE。
6. Capacitance & Energy Storage | 电容与储能
stored per unit potential difference: C = Q/V. For a parallel plate capacitor, C = ε₀A/d.
电容 C 是单位电势差所储存的电荷量：C = Q/V。平行板电容器的电容为 C = ε₀A/d。
C = Q/V C = ε₀A/d E = ½QV = ½CV²
Q²/C. Capacitors in series and parallel follow reciprocal and additive rules respectively.
电容器储存的能量为 E = ½QV = ½CV² = ½Q²/C。电容器的串联遵循倒数相加规则，并联则直接相加。
- Series: 1/Cₑ = 1/C₁ + 1/C₂; Parallel: Cₑ = C₁ + C₂.
- 串联：1/Cₑ = 1/C₁ + 1/C₂；并联：Cₑ = C₁ + C₂。
- Charging: Q = Q₀ (1 - e-t/RC); Discharging: Q = Q₀ e-t/RC.
- 充电：Q = Q₀ (1 - e-t/RC)；放电：Q = Q₀ e-t/RC。
7. Magnetic Fields & Lorentz Force | 磁场与洛伦兹力
v sinθ, where θ is the angle between velocity and field. The direction is given by Fleming's left-hand rule.
磁场对运动电荷施加力：F = Bqv sinθ，其中 θ 是速度与磁场的夹角。方向由弗莱明左手定则确定。
F = Bqv sinθ F = BIL sinθ r = mv / (Bq)
. In a uniform field, a charged particle moves in a circular path with radius r = mv/(Bq).
对于长度为 L 的载流导线，F = BIL sinθ。在匀强磁场中，带电粒子做圆周运动，半径 r = mv/(Bq)。
- Magnetic flux Φ = BA cosθ, flux density B = Φ/A.
- 磁通量 Φ = BA cosθ，磁通密度 B = Φ/A。
8. Electromagnetic Induction | 电磁感应
Faraday' e.m.f. is proportional to the rate of change of magnetic flux linkage: ε = -N ΔΦ/Δt. Lenz's law gives the minus sign, indicating opposition to change.
法拉第定律指出感应电动势与磁通量链的变化率成正比：ε = -N ΔΦ/Δt。负号来自楞次定律，表明感应电动势阻碍磁通量的变化。
ε = -N ΔΦ/Δt ε = Blv (for a rod moving in uniform field)
a field B, the induced e.m.f. is ε = Blv. Transformer equation: Vₚ/Vₛ = Nₚ/Nₛ (for ideal).
当长度为 l 的导体以速度 v 垂直于磁场 B 运动时，感应电动势 ε = Blv。理想变压器公式：Vₚ/Vₛ = Nₚ/Nₛ。
9. Nuclear Physics & Radioactive Decay | 核物理与放射性衰变
Radioactive decay follows an exponential law: N = N₀ e-λt, where λ is the decay constant. Activity A = λN, and half-life T₁/₂ = ln2/λ.
放射性衰变遵循指数规律：N = N₀ e-λt，其中 λ 是衰变常数。活度 A = λN，半衰期 T₁/₂ = ln2/λ。
N = N₀ e-λt A = λN T₁/₂ = ln2 / λ
e binding energy per nucleon relates to stability. In nuclear reactions, mass defect becomes energy.
质能等价：E = mc²。比结合能与稳定性相关。在核反应中，质量亏损转化为能量。
- Fusion and fission reactions conserve charge and nucleon number.
- 聚变和裂变反应中电荷数与核子数守恒。
- Absorbed dose D = E/m (Gray), equivalent dose H = wᵣ D (Sievert).
- 吸收剂量 D = E/m（戈瑞），当量剂量 H = wᵣ D（希沃特）。
10. Quantum Physics & Photoelectric Effect | 量子物理与光电效应
Photon energy E = hf, where h is Planck' quency. The photoelectric effect equation: hf = φ + Eₖ(max), where φ is the work function.
光子能量 E = hf，其中 h 是普朗克常数，f 是频率。光电效应方程为：hf = φ + Eₖ(max)，φ 是逸出功。
E = hf hf = φ + ½ m v²ₘₐₓ p = h/λ
is related to maximum kinetic energy: Eₖ(max) = eVₛ. The de Broglie wavelength is λ = h/p.
截止频率 f₀ = φ/h。遏止电势 Vₛ 与最大动能的关系：Eₖ(max) = eVₛ。德布罗意波长为 λ = h/p。
- Wave-particle duality: particles exhibit wave-like interference.
- 波粒二象性：粒子表现出波动干涉性质。
- Energy levels and photon emission/absorption: ΔE = hf = E₂ - E₁.
- 能级与光子发射/吸收：ΔE = hf = E₂ - E₁。
11. Particle Physics & Conservation Laws | 粒子物理与守恒定律
Particles are classified into hadrons (baryons and mesons) and leptons. Conservation laws include charge, baryon number, lepton number, energy, momentum, and strangeness (where applicable).
粒子分为强子（重子和介子）和轻子。守恒定律涵盖电荷数、重子数、轻子数、能量、动量以及奇异数（在相关过程中）。
p → n + e⁺ + νₑ β⁻ decay: n → p + e⁻ + ν̄ₑ
In beta-minus decay, a neutron turns into a proton, electron, and antineutrino. Quark composition: proton (uud), neutron (udd), pion (u anti-d), etc. The strong force is mediated by gluons.
在β⁻衰变中，中子转变为质子、电子和反中微子。夸克组成：质子（uud）、中子（udd）、π⁺介子（u anti-d）等。强力由胶子传递。
- Lepton number is conserved for each lepton family.
- 各轻子家族的轻子数守恒。
- Annihilation and pair production: E = 2hf = 2mc² (minimum).
- 湮灭与粒子对产生：E = 2hf = 2mc²（最小能量要求）。
12. Astronomy & Cosmology (Optional Topic Extension) | 天文与宇宙学（选学专题拓展）
Hubble' elocity, d distance, and H₀ the Hubble constant. This supports the expansion of the universe.
哈勃定律：v = H₀ d，其中 v 是退行速度，d 是距离，H₀ 是哈勃常数。这为宇宙膨胀提供了证据。
v = H₀ d z = Δλ/λ₀ ≈ v/c (for low speeds)
crowave background radiation (CMBR) has temperature T ≈ 2.73 K, a remnant of the Big Bang.
红移 z = Δλ/λ₀。当 v 远小于 c 时，z ≈ v/c。宇宙微波背景辐射（CMBR）温度 T ≈ 2.73 K，是大爆炸的遗迹。
- Evidence: CMBR, relative abundance of light elements (H, He).
- 证据：CMBR、轻元素的相对丰度（氢、氦）。
- Dark energy and dark matter are indicated by galactic rotation curves and accelerated expansion.
- 星系旋转曲线和加速膨胀表明暗物质与暗能量的存在。
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