📚 A-Level AQA Physics: Formula Summary Handbook | A-Level AQA 物理：公式汇总手册
This handbook brings together the essential formulas for AQA A-Level Physics, covering measurements, mechanics, waves, electricity, fields, thermal physics, nuclear physics and more. Each formula is presented with a short description, and every section follows the same pattern – an English phrase followed by its Chinese equivalent – so you can revise efficiently and reinforce your understanding in both languages.
本手册汇集了 AQA A-Level 物理的核心公式，涵盖测量、力学、波、电学、场、热物理、核物理等内容。每个公式都配有简短说明，每一节也采用相同的英中对照格式，帮助你高效复习、巩固双语理解。
1. Measurements and Uncertainties | 测量与不确定性
Absolute uncertainty in a measurement is the margin of error expressed directly in the unit of the quantity, while relative uncertainty is a percentage that helps compare precision.
测量的绝对不确定度是直接以该量的单位表示的误差范围，而相对不确定度则是一个百分比，便于比较精密程度。
For addition and subtraction, the absolute uncertainties add: ΔZ = ΔA + ΔB (if Z = A ± B).
对于加减运算，绝对不确定度直接相加：ΔZ = ΔA + ΔB（若 Z = A ± B）。
For multiplication and division, percentage uncertainties add: if Z = A × B or Z = A / B, then %ΔZ/Z = %ΔA/A + %ΔB/B.
对于乘除运算，百分比不确定度相加：若 Z = A × B 或 Z = A / B，则 %ΔZ/Z = %ΔA/A + %ΔB/B。
When a quantity is raised to a power n, the percentage uncertainty is multiplied by n: if Q = Aⁿ, %ΔQ/Q = n × (%ΔA/A).
当某量带有 n 次幂时，其百分比不确定度乘以 n：若 Q = Aⁿ，则 %ΔQ/Q = n × (%ΔA/A)。
2. Kinematics | 运动学
The four SUVAT equations describe uniformly accelerated motion in a straight line, where s is displacement, u initial velocity, v final velocity, a acceleration and t time.
四个 SUVAT 方程描述了匀变速直线运动，其中 s 为位移，u 为初速度，v 为末速度，a 为加速度，t 为时间。
v = u + at (final velocity = initial velocity + acceleration × time).
v = u + at（末速度 = 初速度 + 加速度 × 时间）。
s = ut + ½at² (displacement equals initial velocity times time plus half the acceleration times time squared).
s = ut + ½at²（位移 = 初速度 × 时间 + ½ × 加速度 × 时间的平方）。
v² = u² + 2as (relates velocities to displacement without time).
v² = u² + 2as（在不含时间的情况下关联速度与位移）。
s = ½(u + v)t (displacement equals average velocity multiplied by time).
s = ½(u + v)t（位移等于平均速度乘以时间）。
3. Forces and Momentum | 力与动量
Newton’s second law relates resultant force, mass and acceleration; momentum links mass and velocity.
牛顿第二定律将合力、质量和加速度联系起来；动量则将质量和速度联系起来。
F = ma (resultant force = mass × acceleration).
F = ma（合力 = 质量 × 加速度）。
Momentum p = mv, and impulse FΔt = Δp = mv − mu.
动量 p = mv；冲量 FΔt = 动量变化量 Δp = mv − mu。
In collisions and explosions, total momentum is conserved: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂, provided no external resultant force acts.
在碰撞与爆炸中，若无外合力作用，总动量守恒：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。
4. Work, Energy and Power | 功、能与功率
Work is done when a force moves its point of application; energy can be stored as kinetic, potential or elastic energy.
当力使其作用点移动时便做功；能量可以以动能、势能或弹性势能的形式储存。
Work done W = Fs cosθ (where θ is the angle between force and displacement).
做的功 W = Fs cosθ（其中 θ 为力与位移的夹角）。
Kinetic energy Eₖ = ½mv², gravitational potential energy Eₚ = mgh near Earth’s surface.
动能 Eₖ = ½mv²，地表附近的重力势能 Eₚ = mgh。
Elastic potential energy stored in a spring Eₚ = ½FΔx = ½k(Δx)², where k is the spring constant.
弹簧储存的弹性势能 Eₚ = ½FΔx = ½k(Δx)²，其中 k 为劲度系数。
Power P = W / t = Fv (the rate of doing work). Efficiency η = useful output energy / total input energy.
功率 P = W / t = Fv（做功的速率）。效率 η = 有用输出能量 / 总输入能量。
5. Materials | 材料
Hooke’s law, stress, strain and the Young modulus characterise the elastic behaviour of materials.
胡克定律、应力、应变和杨氏模量描述了材料的弹性行为。
Hooke’s law: F = kΔx (force is proportional to extension within the limit of proportionality).
胡克定律：F = kΔx（在比例限度内，力与伸长量成正比）。
Tensile stress σ = F / A, tensile strain ε = ΔL / L (both are ratios with no units, though stress has units Pa).
拉伸应力 σ = F / A，拉伸应变 ε = ΔL / L（均为比值，但应力单位为帕斯卡 Pa）。
Young modulus E = σ / ε = (F/A) / (ΔL/L), describing the stiffness of a material.
杨氏模量 E = σ / ε = (F/A) / (ΔL/L)，表征材料的刚度。
Energy stored per unit volume in an elastically stretched wire is the area under the stress–strain graph, approximately ½ × stress × strain for a linear material.
弹性拉伸的金属丝单位体积储存的能量等于应力–应变图下的面积，对线性材料约为 ½ × 应力 × 应变。
6. Waves and Optics | 波与光学
The wave equation links speed, frequency and wavelength. Refraction, interference and stationary waves have their own key formulas.
波速公式联系了波速、频率和波长。折射、干涉和驻波也有各自的公式。
Wave speed: v = fλ (speed = frequency × wavelength).
波速：v = fλ（波速 = 频率 × 波长）。
Snell’s law: n₁ sinθ₁ = n₂ sinθ₂, and for the critical angle sin θc = n₂/n₁ when n₁ > n₂.
斯涅尔定律：n₁ sinθ₁ = n₂ sinθ₂；当 n₁ > n₂ 时，临界角 sin θc = n₂/n₁。
Young’s double-slit: fringe spacing w = λD / s, where s is the slit separation and D the distance to the screen.
杨氏双缝干涉：条纹间距 w = λD / s，其中 s 为双缝间距，D 为缝到屏的距离。
Diffraction grating: d sinθ = nλ, with d = 1 / N (grating spacing) and n the order of maximum.
衍射光栅：d sinθ = nλ，其中 d = 1 / N（光栅常数），n 为明纹级数。
Frequency of stationary waves: for a string fixed at both ends f = nv/(2L), and for a tube closed at one end f = nv/(4L) (n odd).
驻波频率：两端固定的弦 f = nv/(2L)；一端封闭的管 f = nv/(4L)（n 取奇数）。
7. Electricity | 电学
Basic electrical quantities are connected through Ohm’s law, power equations, and rules for series and parallel circuits.
基本电学量通过欧姆定律、功率公式以及串并联规则联系。
Current: I = ΔQ / Δt. Ohm’s law: V = IR for an ohmic conductor at constant temperature.
电流：I = ΔQ / Δt。欧姆定律：对于恒定温度下的欧姆导体，V = IR。
Resistance and resistivity: R = ρL / A, where ρ is resistivity, L length and A cross-sectional area.
电阻与电阻率：R = ρL / A，其中 ρ 为电阻率，L 为长度，A 为横截面积。
Power: P = IV = I²R = V²/R.
功率：P = IV = I²R = V²/R。
Series: R_total = R₁ + R₂ + … ; parallel: 1/R_total = 1/R₁ + 1/R₂ + …
串联：R_total = R₁ + R₂ + … ；并联：1/R_total = 1/R₁ + 1/R₂ + …
Emf and internal resistance: ε = I(R + r) = V + Ir, where V is the terminal pd.
电动势与内阻：ε = I(R + r) = V + Ir，其中 V 为路端电压。
Potential divider: V_out = V_in × [R₂/(R₁+R₂)].
分压电路：V_out = V_in ×
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