📚 IB & WJEC Physics Formula Compendium | IB 与 WJEC 物理公式汇总手册
This compendium gathers the essential formulae for IB Physics (SL and HL) and WJEC GCE A-Level Physics. Whether you are revising mechanics, waves, electricity, or quantum phenomena, having the key equations at your fingertips will help you solve problems efficiently and deepen your conceptual understanding. All symbols follow standard conventions, and every formula is given in a clear, ready-to-use format.
本手册汇总了 IB 物理（SL 和 HL）与 WJEC GCE A-Level 物理的核心公式。无论你是在复习力学、波动、电学还是量子现象，随时查阅这些关键方程都能帮助你高效解题、加深对概念的理解。所有符号均遵循标准惯例，每条公式都以清晰、可直接使用的形式呈现。
1. Kinematics | 运动学
For uniformly accelerated linear motion, the four SUVAT equations link displacement (s), initial velocity (u), final velocity (v), constant acceleration (a), and time (t).
v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u+v)t
在匀加速直线运动中，四个 SUVAT 方程将位移(s)、初速度(u)、末速度(v)、匀加速度(a)和时间(t)联系在一起。
When a projectile is launched with speed u at an angle θ to the horizontal, its horizontal motion is uniform while its vertical motion is uniformly accelerated.
Horizontal: x = u cosθ × t; Vertical: y = u sinθ × t − ½gt², vy = u sinθ − gt
当抛体以初速 u、仰角 θ 发射时，水平方向为匀速运动，竖直方向为匀加速运动。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s second law states that the net force on a body equals the rate of change of its momentum; for constant mass, this simplifies to F = ma.
F = ma
牛顿第二定律指出物体的合力等于其动量变化率；在质量恒定时简化为 F = ma。
The weight of an object near a planet’s surface is the gravitational force: W = mg, where g is the local gravitational field strength.
W = mg
物体在行星表面附近所受重力为 W = mg，其中 g 为当地重力场强度。
Friction can often be described by f ≤ μR, where μ is the coefficient of friction and R is the normal reaction. The elastic restoring force of a spring follows Hooke’s law: F = kx.
f ≤ μR; F = kx
摩擦力通常用 f ≤ μR 描述，μ 为摩擦系数，R 为法向反作用力。弹簧的弹性回复力遵循胡克定律 F = kx。
3. Energy, Work, and Power | 能量、功与功率
Work done by a constant force acting at an angle θ to the displacement is W = Fs cosθ.
W = Fs cosθ
恒力与位移成 θ 角时，所做的功为 W = Fs cosθ。
Kinetic energy and gravitational potential energy near the surface are given by Ek = ½mv² and Ep = mgh. Elastic potential energy stored in a stretched spring is Ep = ½kx².
Ek = ½mv²; Ep = mgh; Ep = ½kx²
地表附近的动能和重力势能分别为 Ek = ½mv² 和 Ep = mgh。弹簧储存的弹性势能为 Ep = ½kx²。
Power is the rate of doing work: P = ΔW/Δt. For a constant force moving at speed v, it becomes P = Fv.
P = ΔW/Δt; P = Fv
功率是做功的快慢：P = ΔW/Δt。对于以速度 v 运动并受到恒力的情况，P = Fv。
4. Momentum and Impulse | 动量与冲量
Linear momentum is p = mv. Impulse delivered by a constant force over time Δt equals the change in momentum: J = FΔt = Δp.
p = mv; J = FΔt = Δp
线动量为 p = mv。恒力在时间 Δt 内产生的冲量等于动量变化量：J = FΔt = Δp。
In a closed system, total momentum is conserved: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ for a two-body interaction.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
在封闭系统中，总动量守恒：双体相互作用时 m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。
5. Circular Motion | 圆周运动
Angular velocity ω (in rad/s) is related to linear speed by v = ωr. The period T and frequency f satisfy ω = 2πf = 2π/T.
v = ωr; ω = 2πf = 2π/T
角速度 ω（单位 rad/s）与线速度的关系为 v = ωr。周期 T 与频率 f 满足 ω = 2πf = 2π/T。
Centripetal acceleration always points towards the centre: a = v²/r = ω²r. The net inward force providing this acceleration is F = mv²/r = mω²r.
a = v²/r = ω²r; F = mv²/r = mω²r
向心加速度始终指向圆心：a = v²/r = ω²r。提供此加速度的净向心力为 F = mv²/r = mω²r。
6. Gravitational Fields | 引力场
Newton’s law of gravitation between two point masses: F = Gm₁m₂/r², where G is the universal gravitational constant.
F = G (m₁m₂) / r²
两质点间的万有引力定律：F = Gm₁m₂/r²，其中 G 为引力常量。
Gravitational field strength at a distance r from a point mass M is g = F/m = GM/r². The gravitational potential is V = −GM/r.
g = GM/r²; V = −GM/r
距离点质量 M 为 r 处的引力场强度为 g = F/m = GM/r²。引力势为 V = −GM/r。
For a satellite in a stable circular orbit, the centripetal force is provided by gravity, yielding orbital speed v = √(GM/r).
v = √(GM/r)
对于稳定圆轨道上的卫星，引力提供向心力，得出轨道速率 v = √(GM/r)。
7. Thermal Physics | 热物理学
Temperature in kelvin is related to degrees Celsius by T(K) = θ(°C) + 273.15. The ideal gas equation links pressure p, volume V, amount n, and temperature T: pV = nRT.
T(K) = θ(°C) + 273.15; pV = nRT
开尔文温度与摄氏温度的关系为 T(K) = θ(°C) + 273.15。理想气体状态方程关联压强 p、体积 V、物质的量 n 和温度 T：pV = nRT。
The average translational kinetic energy of a gas molecule is related to the absolute temperature: ½ m⟨c²⟩ = (3/2) kT, where k is the Boltzmann constant.
½ m⟨c²⟩ = (3/2) kT
气体分子的平均平移动能与绝对温度的关系为 ½ m⟨c²⟩ = (3/2) kT，k 为玻尔兹曼常量。
Heat transfer without change of state uses Q = mcΔθ; during a phase change, latent heat is Q = mL.
Q = mcΔθ; Q = mL
不发生物态变化时的热传递公式为 Q = mcΔθ；相变时潜热公式为 Q = mL。
8. Oscillations and Waves | 振动与波
For simple harmonic motion, the acceleration is proportional to displacement and opposite in direction: a = −ω²x. Period and frequency are linked by T = 1/f and ω = 2πf.
a = −ω²x; T = 1/f; ω = 2πf
简谐运动中，加速度与位移成正比且方向相反：a = −ω²x。周期与频率的关系为 T = 1/f，且 ω = 2πf。
The wave equation relates speed v, frequency f, and wavelength λ: v = fλ. Refraction obeys Snell’s law: n₁ sinθ₁ = n₂ sinθ₂.
v = fλ; n₁ sinθ₁ = n₂ sinθ₂
波动方程关联波速 v、频率 f 和波长 λ：v = fλ。折射遵循斯涅耳定律：n₁ sinθ₁ = n₂ sinθ₂。
For double-slit interference, fringe separation Δx is given by Δx = λD/d, where D is the slit-to-screen distance and d the slit spacing. Diffraction gratings satisfy d sinθ = nλ.
Δx = λD/d; d sinθ = nλ
双缝干涉条纹间距 Δx 由 Δx = λD/d 给出，D 为缝到屏的距离，d 为缝间距。衍射光栅满足 d sinθ = nλ。
9. Electricity and Circuits | 电学与电路
Electric current is the rate of flow of charge: I = Δq/Δt. Ohm’s law links potential difference, current, and resistance: V = IR.
I = Δq/Δt; V = IR
电流是电荷流动的速率：I = Δq/Δt。欧姆定律关联电势差、电流和电阻：V = IR。
Resistance of a conductor depends on resistivity ρ, length L, and cross-sectional area A: R = ρL/A. Power dissipated in a resistor can be expressed as P = IV = I²R = V²/R.
R = ρL/A; P = IV = I²R = V²/R
导体的电阻取决于电阻率 ρ、长度 L 和横截面积 A：R = ρL/A。电阻耗散的功率可表示为 P = IV = I²
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