📚 Formula & Theorem Quick Reference Handbook | 公式定理速查手册
This quick reference handbook compiles essential formulas and theorems for the Edexcel Pre-U Physics specification. It covers kinematics, dynamics, energy, fields, waves, quantum phenomena, relativity and nuclear physics in a logical sequence. Each entry is presented in an English–Chinese paired style for rapid revision and bilingual understanding.
本速查手册整理了 Edexcel Pre-U 物理考试所需的核心公式与定理，涵盖运动学、动力学、能量、场、波、量子现象、相对论和核物理等内容。每条公式均以英中对照形式呈现，便于快速复习与双语理解。
1. Kinematics & Motion | 运动学
v = u + at gives the final velocity for uniform acceleration.
v = u + at 给出匀加速运动的末速度。
s = ut + ½at² calculates displacement when acceleration is constant.
s = ut + ½at² 计算匀加速直线运动的位移。
v² = u² + 2as links velocity and displacement without time.
v² = u² + 2as 在不涉及时间的情况下联系速度与位移。
s = ½(u + v)t uses the average velocity for displacement.
s = ½(u + v)t 利用平均速度求位移。
Instantaneous velocity and acceleration: v = dx/dt, a = dv/dt = d²x/dt².
瞬时速度与加速度：v = dx/dt, a = dv/dt = d²x/dt²。
Projectile motion: horizontal velocity constant, vertical acceleration g.
抛体运动：水平速度恒定，竖直加速度为 g。
2. Dynamics & Newton's Laws | 动力学与牛顿定律
Newton’s second law: F = ma or F = dp/dt.
牛顿第二定律：F = ma 或 F = dp/dt。
Momentum: p = mv. Impulse: FΔt = Δp.
动量：p = mv。冲量：FΔt = Δp。
Conservation of momentum: total p before collision = total p after.
动量守恒：碰撞前总动量等于碰撞后总动量。
Hooke’s law: F = kx within the elastic limit.
胡克定律：弹性限度内 F = kx。
Friction: Ff ≤ μR, where R is the normal reaction.
摩擦力：Ff ≤ μR，R 为法向反作用力。
3. Work, Energy & Power | 功、能与功率
Work done: W = Fs cosθ, where θ is the angle between force and displacement.
功：W = Fs cosθ，θ 是力与位移的夹角。
Kinetic energy: Ek = ½mv².
动能：Ek = ½mv²。
Gravitational potential energy (uniform field): Ep = mgh.
重力势能（匀强场）：Ep = mgh。
Elastic potential energy: Eelastic = ½kx².
弹性势能：Eelastic = ½kx²。
Work–energy principle: net work done = change in kinetic energy.
功能原理：合力做的功等于动能的变化量。
Power: P = W/t = Fv (when force F and velocity v are parallel).
功率：P = W/t = Fv（当力 F 与速度 v 平行时）。
Efficiency: η = (useful output power)/(input power) × 100%.
效率：η = (有用输出功率)/(输入功率) × 100%。
4. Circular Motion & Gravitation | 圆周运动与引力
Angular velocity: ω = θ/t = 2πf = 2π/T.
角速度：ω = θ/t = 2πf = 2π/T。
Centripetal acceleration: a = v²/r = rω².
向心加速度：a = v²/r = rω²。
Centripetal force: F = mv²/r = mrω².
向心力：F = mv²/r = mrω²。
Newton’s law of gravitation: F = GMm/r².
万有引力定律：F = GMm/r²。
Gravitational field strength: g = F/m; for a point mass, g = GM/r².
引力场强度：g = F/m；对于点质量，g = GM/r²。
Kepler’s third law: T² ∝ r³ for circular orbits: T² = (4π²/GM) r³.
开普勒第三定律：对于圆轨道，T² ∝ r³，即 T² = (4π²/GM) r³。
Gravitational potential energy: U = -GMm/r (with zero at infinity).
引力势能：U = -GMm/r（无穷远处为零）。
5. Oscillations & Waves | 振动与波
Simple harmonic motion (SHM) condition: a = -ω²x.
简谐运动条件：a = -ω²x。
Displacement in SHM: x = A sin(ωt) or x = A cos(ωt).
简谐运动位移：x = A sin(ωt) 或 x = A cos(ωt)。
Velocity in SHM: v = ±ω√(A² - x²).
简谐运动速度：v = ±ω√(A² - x²)。
Period of a mass–spring system: T = 2π√(m/k).
弹簧振子周期：T = 2π√(m/k)。
Period of a simple pendulum: T = 2π√(l/g).
单摆周期：T = 2π√(l/g)。
Wave speed: v = fλ.
波速：v = fλ。
Young’s double-slit fringe spacing: Δx = λD/d, where d is slit separation and D is distance to screen.
杨氏双缝条纹间距：Δx = λD/d，d 为缝距，D 为屏距。
Diffraction grating: d sinθ = nλ, where n is the order.
衍射光栅：d sinθ = nλ，n 为级数。
Refractive index: n = c/v. Snell’s law: n₁ sinθ₁ = n₂ sinθ₂.
折射率：n = c/v。斯涅尔定律：n₁ sinθ₁ = n₂ sinθ₂。
6. Electric Fields & Circuits | 电场与电路
Coulomb’s law: F = (1/4πε₀) Qq/r².
库仑定律：F = (1/4πε₀) Qq/r²。
Electric field strength: E = F/q. For a uniform field: E = V/d.
电场强度：E = F/q。匀强电场：E = V/d。
Electric potential: V = W/q. For a point charge: V = (1/4πε₀) Q/r.
电势：V = W/q。点电荷电势：V = (1/4πε₀) Q/r。
Current: I = ΔQ/Δt.
电流：I = ΔQ/Δt。
Ohm’s law: V = IR.
欧姆定律：V = IR。
Resistance and resistivity: R = ρL/A.
电阻与电阻率：R = ρL/A。
Electric power: P = IV = I²R = V²/R.
电功率：P = IV = I²R = V²/R。
Capacitance: C = Q/V. Energy stored: E = ½CV² = ½QV = ½Q²/C.
电容：C = Q/V。储存能量：E = ½CV² = ½QV = ½Q²/C。
RC time constant: τ = RC. Charge/discharge: Q = Q₀ e-t/RC.
RC 时间常数：τ = RC。充放电：Q = Q₀ e-t/RC。
7. Magnetic Fields & Electromagnetic Induction | 磁场与电磁感应
Force on a moving charge: F = qvB sinθ (Lorentz force).
运动电荷受力：F = qvB sinθ（洛伦兹力）。
Force on a current-carrying conductor: F = BIL sinθ.
载流导线受力：F = BIL sinθ。
Magnetic flux: Φ = BA cosθ.
磁通量：Φ = BA cosθ。
Faraday’s law of induction: ε = -N dΦ/dt.
法拉第电磁感应定律：ε = -N dΦ/dt。
Motional emf (conductor moving perpendicular to field): ε = BLv.
动生电动势（导体垂直切割磁感线）：ε = BLv。
Self-inductance: ε = -L dI/dt. Energy stored in an inductor: E = ½LI².
自感：ε = -L dI/dt。电感储存能量：E = ½LI²。
Ideal transformer: Vs/Vp = Ns/Np = Ip/Is.
理想变压器：Vs/Vp = Ns/Np = Ip/Is。
8. Thermal Physics & Ideal Gases | 热力学与理想气体
Heat capacity: Q = mcΔθ; specific latent heat: Q = mL.
热容：Q = mcΔθ；比潜热：Q = mL。
Ideal gas law: pV = nRT = NkT, where k is Boltzmann’s constant.
理想气体状态方程：pV = nRT = NkT，k 是玻尔兹曼常数。
Kinetic theory: pV = ⅓ N m ⟨c²⟩ and average translational kinetic energy: ½ m ⟨c²⟩ = (3/2) kT.
分子动理论：pV = ⅓ N m ⟨c²⟩，平均平动动能 ½ m ⟨c²⟩ = (3/2) kT。
First law of thermodynamics: ΔU = Q - W (sign convention: W is work done by the system).
热力学第一定律：ΔU = Q - W（符号约定：W 为系统对外做功）。
Adiabatic process for an ideal gas: pVγ = constant, where γ = Cp/Cv.
理想气体绝热过程：pVγ = 常量，其中 γ = Cp/Cv。
Thermal efficiency: η = W/Qh = 1 - Qc/Qh.
热效率：η = W/Qh = 1 - Qc/Qh。
9. Quantum Physics & Atomic Structure | 量子物理与原子结构
Photon energy: E = hf = hc/λ.
光子能量：E = hf = hc/λ。
Photoelectric equation: hf = φ + KEmax, with threshold frequency f₀ = φ/h.
光电效应方程：hf = φ + KEmax，截止频率 f₀ = φ/h。
de Broglie wavelength: λ = h/p = h/mv.
德布罗意波长：λ = h/p = h/mv。
Bohr model: angular momentum mvr = n (h/2π) = nħ.
玻尔模型：角动量 mvr = n (h/2π) = nħ。
Energy levels of hydrogen: En = -13.6 eV / n².
氢原子能级：En = -13.6 eV / n²。
Photon emitted or absorbed during a transition: ΔE = h
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