📚 Year 13 WJEC Physics: Formula & Theorem Quick Reference Handbook | Year 13 WJEC 物理：公式定理速查手册
Welcome to the Year 13 WJEC Physics Formula & Theorem Quick Reference Handbook. This guide compiles essential formulas, relationships and fundamental theorems covered in the A2 units – Oscillations and Nuclei (Unit 3) and Fields and Options (Unit 4). Each section presents key equations with brief explanations, organised for fast revision and practical application. Remember to check unit consistency and use SI units throughout your calculations.
欢迎使用 Year 13 WJEC 物理公式定理速查手册。本指南汇编了 A2 阶段（单元 3 振动与原子核、单元 4 场与选修）涉及的核心公式、关系式和基本定理。每一节都列出关键方程并附简要解释，方便快速复习与实战应用。请注意单位一致性，全部计算采用国际单位制。
1. Circular Motion | 圆周运动
th s divided by the radius r: θ = s / r. Angular velocity ω = Δθ / Δt, with units rad s⁻¹.
角位移 θ（rad）定义为弧长 s 与半径 r 之比：θ = s / r。角速度 ω = Δθ / Δt，单位为 rad s⁻¹。
For uniform circular motion, linear speed v and angular velocity ω are linked by v = ωr.
在匀速圆周运动中，线速度 v 与角速度 ω 的关系为 v = ωr。
Centripetal acceleration a acts towards the centre: a = v² / r = ω²r.
向心加速度 a 指向圆心：a = v² / r = ω²r。
Centripetal force required to maintain circular motion: F = mv² / r = mω²r.
维持圆周运动所需的向心力：F = mv² / r = mω²r。
. For an object in vertical circular motion, energy conservation can be used alongside centripetal force requirements at key points.
周期 T 和频率 f：T = 1/f = 2π / ω。对于竖直面内的圆周运动，在关键位置可结合能量守恒与向心力要求进行分析。
2. Simple Harmonic Motion (SHM) | 简谐运动
onal to displacement x from equilibrium and always directed towards equilibrium: a = −ω²x.
简谐运动发生条件：加速度 a 与离开平衡位置的位移 x 成正比且总指向平衡位置：a = −ω²x。
of time: x = A cos(ωt) or x = A sin(ωt), where A is amplitude and ω is angular frequency.
位移随时间的变化：x = A cos(ωt) 或 x = A sin(ωt)，其中 A 为振幅，ω 为角频率。
Velocity in SHM: v = ±ω √A² − x². Maximum speed vmax = ωA.
简谐运动的速度：v = ±ω √A² − x²。最大速率 vmax = ωA。
Period T = 2π / ω. For a mass-spring system T = 2π √m/k; for a simple pendulum T = 2π √L/g.
周期 T = 2π / ω。弹簧振子 T = 2π √m/k；单摆 T = 2π √L/g。
Total mechanical energy in SHM: Etotal ½ m ω² A² = ½ k A² (for a spring). Energy transitions between kinetic and potential forms.
简谐运动中的总机械能：Etotal = ½ m ω² A² = ½ k A²（弹簧系统）。能量在动能与势能之间转换。
3. Gravitational Fields | 引力场
Newton’s law of gravitation: F = Gm₁m₂ / r², where G = 6.67 × 10⁻¹¹ N m² kg⁻².
牛顿万有引力定律：F = Gm₁m₂ / r²，万有引力常量 G = 6.67 × 10⁻¹¹ N m² kg⁻²。
Gravitational field strength g = F/m. Due to a point mass or spherical body: g = GM / r².
引力场强度 g = F / m。点质量或球体外部：g = GM / r²。
e work done in moving a mass in a field relates to the potential difference ΔV: ΔW = m ΔV.
引力势 V = − GM / r。引力场中移动质量做功与势差相关：ΔW = m ΔV。
Escape velocity from a planet of mass M and radius R: vesc = √2GM / R.
从质量为 M、半径为 R 的行星表面逃逸的速度：vesc = √2GM / R。
Kepler’s third law for circular orbits: T² ∝ r³. Specifically, T² = (4π² / GM) r³, which gives orbital speed v = √GM / r.
开普勒第三定律（圆轨道）：T² ∝ r³。定量为 T² = (4π² / GM) r³，导出轨道速度 v = √GM / r。
4. Electric Fields | 电场
e field strength at a distance r is E = kQ / r², where k = 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻².
电场强度 E = F / q。点电荷 Q 产生的电场强度：E = kQ / r²，其中 k = 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻²。
parallel plates, E = V / d, where V is the potential difference and d is plate separation.
在平行板之间的匀强电场中，E = V / d，V 为电势差，d 为板间距。
Electric potential Ve = kQ / r. The force on a charge q in an electric field is F = qE.
电势 Ve = kQ / r。电荷 q 在电场中所受电场力为 F = qE。
: ΔW = q ΔV, with potential difference ΔV = E d for a uniform field along the field lines.
移动电荷做功：ΔW = q ΔV，匀强电场中沿电场线方向电势差 ΔV = E d。
together with the viscous drag and gravitational force to determine the elementary charge.
密立根油滴实验利用 E = V/d 和 F = qE，结合粘滞阻力和重力来测定元电荷。
5. Capacitance | 电容
For a parallel-plate capacitor with plate area A and separation d, C = ε₀ A / d (vacuum).
电容 C = Q / V，单位为法拉（F）。真空中平行板电容器，极板面积 A、间距 d 时 C = ε₀ A / d。
Energy stored in a capacitor: U = ½ Q V = ½ C V² = ½ Q² / C.
电容器储存的能量：U = ½ Q V = ½ C V² = ½ Q² / C。
Capacitors in parallel: Ceq = C₁ + C₂ + ... ; capacitors in series: 1/Ceq = 1/C₁ + 1/C₂ + ...
电容器并联：Ceq = C₁ + C₂ + ...；电容器串联：1/Ceq = 1/C₁ + 1/C₂ + ...
gh a resistor follow exponential laws: Q = Q₀ exp(−t/RC) during discharge; charging: Q = Qmax (1 − exp(−t/RC)). Time constant τ = RC.
电容器经电阻充放电遵循指数规律：放电时 Q = Q₀ exp(−t/RC)；充电时 Q = Qmax (1 − exp(−t/RC))。时间常数 τ = RC。
6. Magnetic Fields | 磁场
tor in a magnetic field is F = B I L sinθ, where θ is the angle between current and field.
磁通量密度 B 的单位为特斯拉（T）。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。
he centripetal force for circular motion: B Q v = m v² / r, giving radius r = m v / (B Q).
运动电荷在磁场中的受力：F = B Q v sinθ。该力提供圆周运动的向心力：B Q v = m v² / r，回旋半径 r = m v / (B Q)。
e angle between the field and the normal to area A. Flux linkage for a coil of N turns is NΦ.
磁通量 Φ = B A cosθ，θ 为磁场方向与面积法线的夹角。匝数为 N 的线圈的磁链为 NΦ。
= B Q / (2π m), velocity selectors use E = B v when electric and magnetic forces balance.
实际应用：回旋加速器频率 f = B Q / (2π m)，速度选择器在电场力和磁场力平衡时满足 E = B v。
7. Electromagnetic Induction | 电磁感应
N ΔΦ / Δt. Lenz’s law gives the direction of induced current to oppose the change in flux.
法拉第电磁感应定律：感应电动势 ε = − N ΔΦ / Δt。楞次定律确定感应电流方向总是阻碍磁通量的变化。
ving perpendicularly through a uniform B-field with speed v, the induced emf is ε = B L v.
长度为 L 的直导体在匀强磁场 B 中以速度 v 垂直切割磁感线时，感应电动势 ε = B L v。
An ideal transformer satisfies Vₛ / Vₚ = Nₛ / Nₚ and Iₛ / Iₚ = Nₚ / Nₛ, assuming 100% efficiency.
理想变压器满足 Vₛ / Vₚ = Nₛ / Nₚ 和 Iₛ / Iₚ = Nₚ / Nₛ，假设效率为 100%。
Self-inductance L is defined by ε = − L dI/dt. Energy stored in an inductor: U = ½ L I².
自感系数 L 按 ε = − L dI/dt 定义。电感器储存的能量：U = ½ L I²。
8. Ideal Gases and Kinetic Theory | 理想气体与分子动理论
mol⁻¹. Alternatively, pV = NkT where N is number of molecules and k = 1.38 × 10⁻²³ J K⁻¹.
理想气体状态方程：pV = nRT，n 为物质的量（mol），R = 8.31 J K⁻¹ mol⁻¹。也可写为 pV = NkT，N 为分子数，k = 1.38 × 10⁻²³ J K⁻¹。
Kinetic theory links pressure and mean square speed: p = ⅓ (N/V) m ⟨c²⟩, so pV = ⅓ N m ⟨c²⟩.
分子动理论将压强与均方速率联系起来：p = ⅓ (N/V) m ⟨c²⟩，因此 pV = ⅓ N m ⟨c²⟩。
Mean translational kinetic energy of a molecule: ⟨Ek⟩ = ½ m ⟨c²⟩ = (3/2) kT. Temperature is a measure of the average random kinetic energy per molecule.
分子的平均平动动能：⟨Ek⟩ = ½ m ⟨c²⟩ = (3/2) kT。温度是分子平均无规则平动动能的量度。
ystem, and W is work done BY the system (W = p ΔV for gas expansion at constant pressure).
热力学第一定律：ΔU = Q − W，ΔU 为内能增量，Q 为系统吸收的热量，W 为系统对外做的功（恒压膨胀时 W = p ΔV）。
ant, so ΔU = 0 and Q = W. For an adiabatic process, Q = 0, so ΔU = −W and pV^γ = constant.
理想气体等温过程中 T 不变，ΔU = 0，Q = W。绝热过程中 Q = 0，ΔU = −W，且 pV^γ = 常量。
9. Radioactive Decay | 放射性衰变
nstant (s⁻¹) and N is the number of undecayed nuclei. Activity measured in becquerel (Bq).
放射性活度 A = λ N，λ 为衰变常量（s⁻¹），N 为未衰变核的数目。活度单位是贝可（Bq）。
Exponential decay law: N = N₀ exp(−λt) and A = A₀ exp(−λt).
指数衰变规律：N = N₀ exp(−λt) 以及 A = A₀ exp(−λt)。
Half-life T½ is the time for half the nuclei to decay: T½ = ln 2 / λ ≈ 0.693 / λ.
半衰期 T½ 是半数核发生衰变所需的时间：T½ = ln 2 / λ ≈ 0.693 / λ。
After n half-lives, number of nuclei remaining is N = N₀ (½)n. The decay constant and half-life are independent of the amount of material.
经过 n 个半衰期后剩余核数为 N = N₀ (½)n。衰变常量和半衰期与样品量无关。
Radiation types: alpha (α), beta (β⁻, β⁺), gamma (γ). Alpha particles have the highest ionising power; gamma has the greatest penetrating power.
辐射类型：α、β⁻、β⁺、γ。α 粒子电离能力最强；γ 射线穿透能力最强。
10. Mass Defect and Nuclear Energy | 质量亏损与核能
e masses of individual nucleons and the mass of the nucleus: Δm = Z mₚ + N mₙ − m_nucleus.
质量亏损 Δm 是各孤立核子质量之和与原子核质量之差：Δm = Z mₚ + N mₙ − m_核。
Binding energy Ebind ergy per nucleon is a measure of nuclear stability; iron-56 has one of the highest values.
结合能 Ebind = Δm c²。比结合能（每个核子的结合能）是核稳定性的量度；铁-56 的比结合能最大之一。
r reaction is ΔE = Δm c², where Δm = (total mass of reactants) − (total mass of products).
核反应释放的能量为 ΔE = Δm c²，其中 Δm =（反应物总质量）−（生成物总质量）。
Nuclear fission: a heavy nucleus splits into two smaller nuclei, releasing energy and neutrons. Nuclear fusion: light nuclei combine to form a heavier nucleus, releasing energy.
核裂变：重核分裂为两个较小的原子核，释放能量和中子。核聚变：轻核结合成较重的原子核，释放能量。
r processes. Unified atomic mass unit: 1 u = 1.661 × 10⁻²⁷ kg, equivalent to 931.5 MeV/c².
所有核过程遵守质能守恒、电荷守恒和核子数守恒。统一原子质量单位：1 u = 1.661 × 10⁻²⁷ kg，能量当量 931.5 MeV/c²。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图