📚 Physics Revision: Core Formulas and Application Tips | 物理备考：核心公式梳理与应用技巧
Mastering key formulas is essential for physics exams. This article summarises the most important equations across major topics and explains how to apply them confidently.
掌握核心公式是物理备考的关键。本文整理了各主要板块中最重要的方程，并讲解如何自信地运用它们。
1. Kinematics | 运动学
Kinematics describes motion using displacement s, initial velocity u, final velocity v, acceleration a and time t. These equations assume constant acceleration.
运动学用位移 s、初速度 u、末速度 v、加速度 a 和时间 t 描述运动。以下公式均假设加速度恒定。
v = u + at
s = ½(u + v)t
s = ut + ½at²
v² = u² + 2as
Choose the equation that contains the three known variables and the one unknown you need. Always check the sign of acceleration when the object slows down.
选择包含三个已知量和待求量的公式。当物体减速时，务必注意加速度的符号。
| Convert units before substituting: 1 km/h = (1000/3600) m/s. | 代入前先换算单位：1 km/h = (1000/3600) m/s。 |
| For projectile motion, treat horizontal and vertical motion separately. | 抛体运动应分别处理水平与竖直方向。 |
2. Forces and Newton's Laws | 力与牛顿定律
Newton's second law relates net force to mass and acceleration. The weight of an object is the gravitational force acting on it.
牛顿第二定律将合外力、质量和加速度联系起来。物体的重量是作用在其上的重力。
F = ma
W = mg
F = μN (friction)
e forces into perpendicular components, then apply F = ma along each direction separately.
先画受力分析图，将力沿垂直方向分解，再沿各方向分别应用 F = ma。
| The normal reaction N is not always equal to mg on slopes or lifts. | 在斜面或电梯中，支持力 N 不一定等于 mg。 |
| Use F = ma for the whole system when bodies are connected by a light string. | 轻绳连接多个物体时，可用整体法应用 F = ma。 |
3. Work, Energy and Power | 功、能量与功率
Work is done when a force moves an object. Energy changes are calculated using gravitational potential and kinetic energy formulas.
力使物体发生位移时做功。能量变化通过重力势能和动能公式计算。
W = Fd cos θ
Eₖ = ½mv²
Eₚ = mgh
P = W/t = Fv
he change in potential energy. For power, use P = Fv when force and velocity are parallel.
注意：保守力做功等于势能变化。功率公式 P = Fv 在力与速度同向时使用。
| If θ = 90°, no work is done by the force. | 若 θ = 90°，力不做功。 |
| In energy conservation, include all forms: kinetic, potential, thermal, etc. | 能量守恒时要包含所有形式：动能、势能、热能等。 |
4. Momentum and Collisions | 动量与碰撞
Momentum is the product of mass and velocity. The principle of conservation of momentum applies when no external resultant force acts.
动量是质量与速度的乘积。当合外力为零时，动量守恒定律成立。
p = mv
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
For a perfect elastic collision between equal masses, the particles simply exchange velocities.
质量相同的两个物体发生完全弹性碰撞时，它们会交换速度。
| Use momentum conservation for explosions and collisions, but check whether kinetic energy is conserved. | 爆炸和碰撞问题使用动量守恒，但需检查动能是否守恒。 |
| For impulse, the area under a force-time graph equals the change in momentum. | 对于冲量，力-时间图像下的面积等于动量变化。 |
5. Circular Motion and Gravitation | 圆周运动与万有引力
Uniform circular motion requires a centripetal acceleration directed towards the centre. Gravitational force provides this for orbiting bodies.
匀速圆周运动需要指向圆心的向心加速度。万有引力为天体提供这种加速度。
a = v²/r = ω²r
F = mv²/r
F = GMm/r²
ω = 2π/T = 2πf
In orbit problems, set gravitational force equal to the required centripetal force. For satellites, the period T is related to radius r by Kepler's third law.
在轨道问题中，令万有引力等于所需的向心力。对卫星，周期 T 与半径 r 的关系遵循开普勒第三定律。
| Centripetal force is not an extra force; it is the resultant of other forces. | 向心力不是额外力，而是其他力的合力。 |
| The gravitational field strength g = GM/r² at a point. | 某点的重力场强度 g = GM/r²。 |
6. Oscillations | 简谐运动
Simple harmonic motion (SHM) occurs when acceleration is proportional to displacement and directed towards equilibrium.
简谐运动 (SHM) 的加速度与位移成正比，且方向指向平衡位置。
a = -ω²x
x = A cos(ωt)
T = 2π√m/k (mass-spring)
T = 2π√l/g (pendulum)
For a mass-spring system, the period is independent of amplitude. For a pendulum, small oscillations are isochronous.
弹簧振子的周期与振幅无关。单摆在小角度下做等时摆动。
| Velocity is maximum at equilibrium, zero at extremities. | 速度在平衡位置最大，在端点为零。 |
| Energy in SHM is conserved: elastic potential + kinetic = constant. | 简谐运动机械能守恒：弹性势能 + 动能 = 常量。 |
7. Thermodynamics | 热力学
Thermodynamics deals with heat, work, internal energy and the ideal gas law. The first law expresses energy conservation.
热力学处理热、功、内能和理想气体定律。热力学第一定律表达能量守恒。
ΔU = Q - W
PV = nRT
W = PΔV (isobaric)
31 J/(mol·K). Temperatures must be in kelvin. For an isothermal process, ΔU = 0, so Q = W.
理想气体方程中，R = 8.31 J/(mol·K)。温度单位必须用开尔文。等温过程中 ΔU = 0，因此 Q = W。
| Sign conventions: work done by the gas is positive in ΔU = Q - W. | 符号规定：在 ΔU = Q - W 中，气体对外做功取正。 |
| For adiabatic processes, Q = 0, so ΔU = -W. | 绝热过程中 Q = 0，所以 ΔU = -W。 |
8. Electric Fields and Circuits | 电场与电路
Electric fields exert forces on charges. Circuit analysis uses Ohm's law and power relationships.
电场对电荷施加力。电路分析使用欧姆定律和功率关系。
E = F/q
F = kQ₁Q₂/r²
V = IR
P = IV = I²R = V²/R
= CV and stored energy is ½CV². In series, capacitors combine differently from resistors.
对电容器，Q = CV，储存能量为 ½CV²。串联电容的合并方式与电阻不同。
| In series resistors add: R = R₁ + R₂; in parallel: 1/R = 1/R₁ + 1/R₂. | 电阻串联相加：R = R₁ + R₂；并联满足 1/R = 1/R₁ + 1/R₂。 |
| The electric field between parallel plates is uniform, E = V/d. | 平行板之间的电场均匀，E = V/d。 |
9. Magnetic Fields and Electromagnetic Induction | 磁场与电磁感应
Magnetic fields exert forces on moving charges and currents. Electromagnetic induction is described by Faraday's and Lenz's laws.
磁场对运动电荷和电流施加力。电磁感应由法拉第定律和楞次定律描述。
F = BIl sin θ
F = qvB sin θ
ε = -NΔΦ/Δt
Φ = BA cos θ
The negative sign in Faraday's equation represents Lenz's law, which ensures energy conservation. Use the right-hand rule for current direction.
法拉第方程中的负号表示楞次定律，确保能量守恒。判断电流方向使用右手定则。
| The force on a charge is always perpendicular to both v and B, giving circular motion. | 洛伦兹力始终垂直于 v 和 B，使电荷做圆周运动。 |
| For a coil rotating in a magnetic field, induced emf varies sinusoidally. | 线圈在磁场中转动时，感应电动势按正弦规律变化。 |
10. Waves and Optics | 波动与光学
Waves transfer energy without transferring matter. Key relationships involve wave speed, frequency, wavelength and interference.
波传递能量而不传递物质。关键关系涉及波速、频率、波长和干涉。
v = fλ
n₁ sin θ₁ = n₂ sin θ₂
d sin θ = nλ (diffraction grating)
acent nodes are separated by λ/2. In double-slit interference, fringe spacing is w = λD/a.
在驻波中，相邻波节相距 λ/2。在双缝干涉中，条纹间距 w = λD/a。
| When light moves from a rarer to a denser medium, it bends towards the normal. | 光从光疏介质进入光密介质时，会向法线方向偏折。 |
| For total internal reflection, the angle of incidence must exceed the critical angle. | 发生全反射时，入射角必须大于临界角。 |
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