📚 A-Level Physics: Formula Summary Handbook | A-Level 物理：公式汇总手册
This handbook compiles the essential formulae for A-Level Physics, covering mechanics, waves, electricity, thermal physics, fields, and nuclear physics. Each formula is presented with clear notation and units, accompanied by concise explanations to aid revision and problem-solving. Use this guide alongside your syllabus to master quantitative reasoning in physics.
本手册汇编了A-Level物理的核心公式，涵盖力学、波、电学、热物理、场以及核物理等内容。每个公式均标注了清晰的符号和单位，并配以简要说明，以帮助复习和解题。请将本手册与课程大纲结合使用，掌握物理中的定量推理。
1. Kinematics | 运动学
The SUVAT equations describe motion with constant acceleration in a straight line. They link displacement s, initial velocity u, final velocity v, acceleration a, and time t. It is vital to define a positive direction, especially when dealing with gravity. For vertical motion near Earth’s surface, a = –g if upward is taken as positive (g = 9.81 m s⁻²).
SUVAT方程描述匀变速直线运动，关联位移s、初速度u、末速度v、加速度a和时间t。在处理重力时必须规定正方向。若取向上为正，则竖直运动中的加速度a = –g，其中g = 9.81 m s⁻²。
v = u + at
s = ut + ½at²
s = (u + v)t / 2
v² = u² + 2as
a = –g (upwards positive)
2. Dynamics | 动力学
Newton’s second law states that the resultant force on an object equals the rate of change of its momentum. For constant mass, this simplifies to F = ma. Weight is the gravitational force on a mass: W = mg. Friction, tension, and normal contact forces also act in mechanical systems, often requiring free-body diagrams to resolve components.
牛顿第二定律指出，作用在物体上的合力等于其动量的变化率。对于质量不变的情况，简化为F = ma。重量是质量所受的重力：W = mg。在力学系统中还需考虑摩擦力、张力和法向接触力，通常需要借助受力分析图分解各分量。
F = ma
W = mg
3. Work, Energy and Power | 功、能与功率
Work done by a constant force is W = Fs cos θ, where θ is the angle between the force and displacement. Kinetic energy is KE = ½mv², and gravitational potential energy change near Earth’s surface is ΔEₚ = mgΔh. Power, the rate of doing work, can be written as P = W/t or, for constant velocity, P = Fv. Conservation of energy applies in isolated systems, and efficiency is useful output over total input.
恒力做功为W = Fs cos θ，其中θ为力与位移的夹角。动能为Eₖ = ½mv²，地表附近的重力势能变化为ΔEₚ = mgΔh。功率是做功的速率，可表示为P = W/t，或者在匀速条件下P = Fv。孤立系统满足能量守恒，效率定义为有用输出与总输入的比值。
W = Fs cos θ
Eₖ = ½mv²
ΔEₚ = mgΔh
P = W/t = Fv
4. Momentum | 动量
Linear momentum is p = mv. The impulse of a force equals the change in momentum: FΔt = Δp. In collisions or explosions, the total momentum of a closed system is conserved, i.e., total momentum before equals total momentum after. For two objects, m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂, taking directions into account.
动量为p = mv。力的冲量等于动量的变化：FΔt = Δp。在碰撞或爆炸中，封闭系统的总动量守恒，即碰撞前总动量等于碰撞后总动量。对于两个物体，考虑方向时有m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。
p = mv
FΔt = Δp
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
5. Materials | 材料
Stress σ = F/A and strain ε = ΔL/L₀ describe deformation. Young’s modulus E = σ/ε measures stiffness for materials obeying Hooke’s law. Within the elastic limit, the force–extension relation is F = kx, and the elastic potential energy stored is E = ½FΔL = ½k(ΔL)². The stress–strain graph shows the elastic limit, yield point, and ultimate tensile strength.
应力σ = F/A和应变ε = ΔL/L₀描述形变。杨氏模量E = σ/ε衡量遵循胡克定律材料的刚度。在弹性限度内，力与伸长量的关系为F = kx，储存的弹性势能为E = ½FΔL = ½k(ΔL)²。应力–应变图显示弹性极限、屈服点和极限抗拉强度。
σ = F/A
ε = ΔL/L₀
E = σ/ε
F = kx
E = ½FΔL = ½k(ΔL)²
6. Waves | 波
The wave equation v = fλ links speed, frequency, and wavelength. Refractive index n = sin i / sin r = c/v, and total internal reflection occurs when the angle of incidence exceeds the critical angle sin c = 1/n. For diffraction gratings, the maxima satisfy d sinθ = nλ. In double-slit interference, fringe spacing x is given by λ = ax/D, where a is slit separation and D is the distance to the screen.
波速公式v = fλ关联波速、频率和波长。折射率n = sin i / sin r = c/v，当入射角大于临界角sin c = 1/n时发生全内反射。对于衍射光栅，明纹满足d sinθ = nλ。在双缝干涉中，条纹间距x由λ = ax/D给出，其中a为缝距，D为缝到屏的距离。
v = fλ
n = sin i / sin r = c/v
sin c = 1/n
d sinθ = nλ
λ = ax/D
7. Electricity | 电学
Current is the rate of charge flow: I = ΔQ/Δt. Potential difference V = W/Q, and resistance R = V/I. Resistivity ρ relates to resistance and geometry: ρ = RA/L. Electrical power can be expressed as P = IV = I²R = V²/R. For a source with emf ε and internal resistance r, the terminal pd is V = ε – Ir, and the circuit equation is ε = I(R + r).
电流是电荷流动的速率：I = ΔQ/Δt。电势差V = W/Q，电阻R = V/I。电阻率ρ与电阻和几何尺寸的关系为ρ = RA/L。电功率可表示为P = IV = I²R = V²/R。对于具有电动势ε和内阻r的电源，端电压为V = ε – Ir，电路方程为ε = I(R + r)。
I = ΔQ/Δt
V = W/Q
R = V/I
ρ = RA/L
P = IV = I²R = V²/R
ε = I(R + r), V = ε – Ir
8. Circuits | 电路
Kirchhoff’s laws govern circuit analysis: the sum of currents entering a junction is zero (ΣI = 0), and the sum of the emfs in a closed loop equals the sum of the pds (Σε = ΣIR). For resistors in series, R_total = R₁ + R₂ + …; in parallel, 1/R_total = 1/R₁ + 1/R₂ + … . A potential divider splits voltage: V_out = V_in × R₂/(R₁ + R₂).
基尔霍夫定律用于电路分析：流入节点的电流代数和为零（ΣI = 0），闭合回路中电动势的代数和等于各元件电位差的代数和（Σε = ΣIR）。电阻串联时R_total = R₁ + R₂ + …；并联时1/R_total = 1/R₁ + 1/R₂ + …。分压器按V_out = V_in × R₂/(R₁ + R₂)分配电压。
ΣI = 0 (junction)
Σε = ΣIR (loop)
Series: R = R₁ + R₂ + …
Parallel: 1/R = 1/R₁ + 1/R₂ + …
V_out = V_in × R₂/(R₁ + R₂)
9. Thermal Physics | 热物理
The ideal gas law is pV = nRT = NkT, where n is the number of moles, N the number of molecules, and k the Boltzmann constant. The average translational kinetic energy of a molecule is ½m
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