📚 Pre-U CAIE Physics: Formulas and Theorems Quick Reference | Pre-U CAIE 物理：公式定理速查手册
This comprehensive quick-reference guide covers the essential formulas and theorems required for the Cambridge Pre-U Physics examination. Each section focuses on a core topic, presenting key relationships in a clear, bilingual format. Whether you are revising for an exam or need a handy summary, this handbook will help reinforce your understanding of fundamental physics principles.
这本综合速查手册涵盖了剑桥Pre-U物理考试所需的核心公式和定理。每个部分聚焦一个关键主题，以清晰的中英双语形式呈现重要关系。无论是为考试复习还是需要一个便捷的总结，这本手册都将帮助你巩固对基本物理原理的理解。
1. Mechanics and Dynamics | 力学与动力学
, where v is final velocity, u is initial velocity, a is constant acceleration, t is time.
匀加速运动方程(suvat): v = u + at, 其中v为末速度, u为初速度, a为恒定加速度, t为时间。
Displacement: s = ut + ½ at².
位移: s = ut + ½ at²。
Velocity-displacement relation: v² = u² + 2as.
速度-位移关系: v² = u² + 2as。
Average velocity expression: s = (u + v)t / 2.
平均速度表达式: s = (u + v)t / 2。
Newton's second law of motion: F = m a, where F is net force, m is mass, a is acceleration.
牛顿第二定律: F = m a, F为合力, m为质量, a为加速度。
Newton's third law: If body A exerts a force on body B, then B exerts an equal and opposite force on A.
牛顿第三定律: 如果物体A对物体B施加一个力, 那么B对A施加一个大小相等、方向相反的力。
ore collision = total momentum after collision, provided no external resultant force acts.
动量: p = m v。动量守恒: 若无合外力作用, 碰撞前总动量 = 碰撞后总动量。
Impulse: F Δt = Δp, where impulse equals change in momentum.
冲量: F Δt = Δp, 冲量等于动量的变化量。
ne by a constant force: W = F d cosθ, where θ is the angle between force and displacement.
恒力做功: W = F d cosθ, θ为力与位移之间的夹角。
Kinetic energy: KE = ½ m v². Gravitational potential energy near Earth's surface: GPE = m g h.
动能: KE = ½ m v²。近地表重力势能: GPE = m g h。
et work done = change in kinetic energy, or W = ΔKE + ΔPE against non-conservative forces.
功能原理: 合外力做功等于动能的变化, 或考虑非保守力时W = ΔKE + ΔPE。
Power: P = W / t, and for motion at constant velocity, P = F v.
功率: P = W / t, 匀速运动时 P = F v。
Hooke' spring constant, x is extension. Elastic potential energy stored in a spring: E = ½ k x².
胡克定律: F = k x, k为劲度系数, x为伸长量。弹簧弹性势能: E = ½ k x²。
ot and θ is the angle between F and the lever arm. Equilibrium requires ΣF = 0 and Στ = 0.
力矩: τ = F d sinθ, d为转轴到力作用线的距离, θ为力与力臂的夹角。平衡条件: ΣF = 0 且 Στ = 0。
2. Circular Motion and Gravitation | 圆周运动与引力
displacement and speed: ω = θ / t. Relationship between linear and angular speed: v = r ω.
角位移与角速度: ω = θ / t。线速度与角速度关系: v = r ω。
ntripetal acceleration: a = v² / r = r ω². Centripetal force: F = m a = m v² / r = m r ω².
向心加速度: a = v² / r = r ω²。向心力: F = m a = m v² / r = m r ω²。
Newton's law of gravitation: F = G M m / r², where G is the universal gravitational constant.
万有引力定律: F = G M m / r², G为万有引力常数。
Gravitational field strength: g = F / m = G M / r².
引力场强度: g = F / m = G M / r²。
tellite in circular orbit: centripetal force provided by gravity, giving orbital speed v = √G M / r.
圆轨道卫星: 引力提供向心力, 轨道速率 v = √G M / r。
Kepler's third law (derived): T² = (4π² / G M) r³, where T is orbital period.
开普勒第三定律 (推导): T² = (4π² / G M) r³, T为轨道周期。
Gravitational potential energy: U = - G M m / r. Escape speed from a planet: vesc = √2 G M / R.
引力势能: U = - G M m / r。行星逃逸速度: vesc = √2 G M / R。
3. Simple Harmonic Motion | 简谐运动
al to displacement x from equilibrium and always directed towards equilibrium: a = - ω² x.
简谐运动定义: 加速度a与偏离平衡位置的位移x成正比, 且总指向平衡位置: a = - ω² x。
f time: x = A sin(ω t) or x = A cos(ω t), where A is amplitude and ω is angular frequency.
位移时间关系: x = A sin(ω t) 或 x = A cos(ω t), A为振幅, ω为角频率。
Velocity: v = ± ω √A² - x²; maximum speed vmax = ω A.
速度: v = ± ω √A² - x²; 最大速率 vmax = ω A。
Acceleration: a = - ω² x; maximum acceleration amax = ω² A.
加速度: a = - ω² x; 最大加速度 amax = ω² A。
Period and frequency: T = 1 / f, ω = 2π f = 2π / T.
周期与频率: T = 1 / f, ω = 2π f = 2π / T。
Mass-spring system: T = 2π √m / k, where k is spring constant.
弹簧振子周期: T = 2π √m / k, k为劲度系数。
Simple pendulum (small amplitude): T = 2π √L / g, where L is length.
单摆(小角度): T = 2π √L / g, L为摆长。
Energy in SHM: total energy Etotal = ½ k A² (spring system) or ½ m ω² A²; kinetic plus potential energy constant.
简谐运动中的能量: 总能量 Etotal = ½ k A² (弹簧振子) 或 ½ m ω² A²; 动能与势能之和守恒。
4. Thermal Physics | 热物理学
8.31 J mol⁻¹ K⁻¹. Also p V = N k T, with N = number of molecules, k = Boltzmann constant.
理想气体方程: p V = n R T, n为摩尔数, R = 8.31 J mol⁻¹ K⁻¹。同时 p V = N k T, N为分子数, k为玻尔兹曼常数。
Kinetic theory model: p V = 1/3 N m ⟨c²⟩, where m is molecular mass and ⟨c²⟩ is mean square speed. Average translational kinetic energy: ⟨KE⟩ = 3/2 k T.
分子运动论模型: p V = 1/3 N m ⟨c²⟩, m为分子质量, ⟨c²⟩为方均速率。平均平动动能: ⟨KE⟩ = 3/2 k T。
, where ΔU is change in internal energy, Q is heat supplied to system, W is work done on system. (Sign convention may vary; exam clarity required.)
热力学第一定律: ΔU = Q + W, ΔU为内能变化, Q为系统吸收的热量, W为外界对系统做的功。(符号约定可能不同, 考试中需明确。)
nstant, p V = constant. Adiabatic process: no heat transfer, p V^γ = constant, where γ = Cp / Cv.
等温过程: 温度恒定, p V = 常数。绝热过程: 无热传递, p V^γ = 常数, γ = Cp / Cv。
Efficiency of a heat engine: η = useful work output / Qh = (Qh - Qc) / Qh. Maximum Carnot efficiency: η_Carnot = 1 - Tc / Th (temperatures in kelvin).
热机效率: η = 有用功输出 / Qh = (Qh - Qc) / Qh。最大卡诺效率: η_Carnot = 1 - Tc / Th (温度用开氏温标)。
Entropy change in a reversible process: ΔS = Q / T.
可逆过程的熵变: ΔS = Q / T。
5. Electric Fields and Capacitance | 电场与电容
Coulomb's law: F = k Q q / r², where k = 1/(4π ε₀) and ε₀ is permittivity of free space.
库仑定律: F = k Q q / r², 其中 k = 1/(4π ε₀), ε₀为真空介电常数。
Electric field strength: E = F / q. For a point charge, E = k Q / r².
电场强度: E = F / q。点电荷电场: E = k Q / r²。
c potential: V = k Q / r (taking zero at infinity). Potential energy of a charge: U = q V.
电势: V = k Q / r (取无穷远为零势能点)。电荷的电势能: U = q V。
plates: E = V / d, where V is p.d. and d is plate separation. Force on a charge: F = q E.
平行板间的匀强电场: E = V / d, V为电压, d为板间距。电荷受力: F = q E。
Capacitance: C = Q / V. For a parallel-plate capacitor, C = ε₀ A / d.
电容: C = Q / V。平行板电容器: C = ε₀ A / d。
Energy stored in a capacitor: W = ½ C V² = ½ Q V = ½ Q² / C.
电容器储存的能量: W = ½ C V² = ½ Q V = ½ Q² / C。
Combination rules: series, 1/C = Σ 1/Ci; parallel, C = Σ Ci.
电容组合规律: 串联: 1/C = Σ 1/Ci; 并联: C = Σ Ci。
Charging/discharging of capacitor: charge Q = Q₀ e-t / RC, time constant τ = R C.
电容器充/放电: 电荷 Q = Q₀ e-t / RC, 时间常数 τ = R C。
6. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
tor in a magnetic field: F = B I L sinθ, where θ is angle between B and current direction.
磁场对载流导线的作用力: F = B I L sinθ, θ为B与电流方向的夹角。
Force on a moving charge: F = B q v sinθ.
运动电荷在磁场中受力: F = B q v sinθ。
Magnetic flux: Φ = B A cosθ, where θ is angle between B and normal to area A.
磁通量: Φ = B A cosθ, θ为B与面积A法线间的夹角。
Faraday's law of induction: induced e.m.f. ε = - dΦ / dt. Lenz's law: the direction of induced current opposes the change in flux producing it.
法拉第电磁感应定律: 感应电动势 ε = - dΦ / dt。楞次定律: 感应电流的方向总是阻碍引起它的磁通量变化。
For a transformer: Vs / Vp = Ns / Np, and for an ideal transformer, power in primary = power in secondary, i.e. Vp Ip = Vs Is.
变压器: Vs / Vp = Ns / Np, 理想变压器原边功率等于副边功率: Vp Ip = Vs Is。
Self-inductance: ε = - L dI / dt. Energy stored in an inductor: E = ½ L I².
自感: ε = - L dI / dt。电感存储的能量: E = ½ L I²。
Hall effect: Hall voltage VH = B I / (n q t), where n is charge carrier density, t is thickness.
霍尔效应: 霍尔电压 VH = B I / (n q t), n为载流子浓度, t为厚度。
7. Waves and Optics | 波与光学
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