📚 Pre-U AQA Physics: Formula and Theorem Quick Reference Handbook | Pre-U AQA 物理：公式定理速查手册
This handbook compiles the essential formulas, theorems and key constants needed for the Pre-U AQA Physics examination. Each entry is presented with a concise explanation in English followed by its Chinese translation, allowing you to revise concepts efficiently and deepen your understanding of the underlying principles. Use this quick reference to reinforce your memory and to check your working during practice.
本手册汇编了 Pre-U AQA 物理考试所需的核心公式、定理和关键常数。每一条目均配有简要的英文解释及对应的中文翻译，帮助你高效复习概念并加深对物理原理的理解。请使用此速查手册巩固记忆并在练习中核查你的解题过程。
1. Kinematics | 运动学
Kinematics describes motion without considering forces. The following equations apply to motion with constant acceleration along a straight line.
运动学描述不考虑力的情况下的运动。下列方程适用于匀加速直线运动。
The velocity–time relation gives the final velocity after time t.
v = u + at
速度–时间关系式给出经过时间 t 后的末速度。
Displacement can be expressed in terms of initial velocity, acceleration and time.
s = ut + ½at²
位移可以用初速度、加速度和时间表示。
Eliminating time from the primary equations yields a relation between velocities and displacement.
v² = u² + 2as
消去时间可从基本方程导出初末速度与位移的关系。
The average-velocity form is useful when time is known but acceleration is not explicitly required.
s = ½(u + v)t
当已知时间而不需要显式加速度时，平均速度公式非常方便。
2. Dynamics | 动力学
Dynamics links forces to the motion of objects. Newton’s laws of motion are the foundation.
动力学将力与物体的运动联系起来。牛顿运动定律是基础。
Newton’s second law states that resultant force equals mass times acceleration.
F = ma
牛顿第二定律指出合力等于质量乘以加速度。
Weight is the gravitational force on a mass near a planet’s surface.
W = mg
重力是行星表面附近的物体所受的引力。
The maximum static friction and kinetic friction are proportional to the normal reaction force.
f = μR
最大静摩擦力和动摩擦力均与法向反作用力成正比。
On an inclined plane, the component of weight parallel to the slope is mg sin θ.
F∥ = mg sin θ
在斜面上，重力平行于斜面的分量为 mg sin θ。
3. Energy, Work & Power | 能量、功与功率
Energy is a conserved quantity that can be transferred by work or heating. These formulas quantify mechanical energy transfers.
能量是一个守恒量，可以通过做功或热传递进行转移。以下公式量化了机械能的传递。
Work done by a constant force is the product of force and displacement in the direction of the force.
W = Fd cos θ
恒力做的功等于力与沿力方向位移的乘积。
Kinetic energy depends on mass and speed.
KE = ½mv²
动能取决于质量和速率。
Change in gravitational potential energy near Earth’s surface.
ΔGPE = mgΔh
地球表面附近重力势能的变化。
Power is the rate of doing work, also expressible as force times velocity.
P = W/t = Fv
功率是做功的速率，也可表示为力乘以速度。
Efficiency compares useful output power to total input power.
η = (Pout / Pin) × 100%
效率比较有用输出功率与总输入功率。
4. Momentum & Impulse | 动量与冲量
Momentum is conserved in isolated systems, making it a powerful tool for analysing collisions and explosions.
动量在孤立系统中守恒，这使其成为分析碰撞和爆炸的强大工具。
Linear momentum is the product of mass and velocity.
p = mv
线动量是质量与速度的乘积。
Impulse equals change in momentum and also the average force multiplied by time.
Δp = FΔt
冲量等于动量的变化，也等于平均力乘以时间。
Conservation of momentum for a two-body collision.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
两体碰撞的动量守恒。
For perfectly elastic collisions, relative speed of approach equals relative speed of separation.
v₂ − v₁ = −(u₂ − u₁)
对于完全弹性碰撞，接近的相对速率等于分离的相对速率。
5. Circular Motion & Gravitation | 圆周运动与引力
Uniform circular motion involves a centripetal force directed towards the centre. Newton’s law of gravitation governs celestial mechanics.
匀速圆周运动需要一个指向中心的向心力。牛顿万有引力定律支配天体力学。
Angular velocity relates linear speed and radius.
v = rω
角速度将线速率与半径联系起来。
Centripetal acceleration can be expressed in terms of v or ω.
a = v²/r = rω²
向心加速度可用 v 或 ω 表示。
The centripetal force required for circular motion.
F = mv²/r = mrω²
圆周运动所需的向心力。
Newton’s law of universal gravitation.
F = Gm₁m₂/r²
牛顿万有引力定律。
Gravitational field strength at a distance from a point mass.
g = GM/r²
点质量外某处的引力场强度。
Kepler’s third law for planetary orbits (circular approximation).
T² ∝ r³
开普勒第三定律的行星轨道形式（圆轨道近似）。
6. Simple Harmonic Motion & Waves | 简谐运动与波
SHM is oscillatory motion where acceleration is proportional to displacement and directed towards equilibrium. Waves transfer energy without net transfer of matter.
简谐运动是一种加速度与位移成正比且指向平衡位置的振荡运动。波传递能量而无物质净转移。
Defining equation for SHM.
a = −ω²x
简谐运动的定义方程。
Period of a mass–spring system.
T = 2π√(m/k)
弹簧振子的周期。
Period of a simple pendulum for small amplitudes.
T = 2π√(L/g)
小角度单摆的周期。
Wave speed relates frequency and wavelength.
v = fλ
波速将频率和波长联系起来。
Young’s double-slit fringe separation.
Δx = λD / s
杨氏双缝干涉条纹间距。
Diffraction grating equation for maxima.
d sin θ = nλ
衍射光栅的极大方程。
Snell’s law of refraction.
n₁ sin θ₁ = n₂ sin θ₂
斯涅尔折射定律。
7. Electric Fields & Potential | 电场与电势
Electric fields describe the force experienced by a charge. Potential is a scalar quantity defined as work done per unit charge.
电场描述电荷所受的力。电势是一个标量，定义为单位电荷所做的功。
Field strength is force per unit positive charge.
E = F / q
电场强度是单位正电荷所受的力。
Field due to a point charge.
E = kQ / r² (where k = 1/(4πε₀))
点电荷的电场。
Electric potential at a distance from a point charge.
V = kQ / r
点电荷外某处的电势。
Work done in moving a charge through a potential difference.
W = qΔV
电荷在电势差间移动时所做的功。
Field strength between parallel plates (uniform field).
E = V / d
平行板间的匀强电场强度。
8. Capacitance | 电容
Capacitors store charge and energy in an electric field. Their behaviour in circuits is governed by exponential charging and discharging curves.
电容器在电场中储存电荷和能量。它们在电路中的行为由指数充放电曲线描述。
Capacitance is defined as charge stored per unit potential difference.
C = Q / V
电容定义为储存的电荷与电势差之比。
For a parallel-plate capacitor with dielectric.
C = ε₀εᵣ A / d
具有介质的平行板电容器公式。
Energy stored in a capacitor can be expressed in three equivalent forms.
E = ½QV = ½CV² = ½Q²/C
电容器储存的能量有三种等价表达形式。
Time constant for an RC circuit.
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