📚 Common Physics Formulas Compilation | 物理常用公式汇编
Physics formulas are the concise language of nature, capturing essential relationships between measurable quantities. This compilation brings together the most frequently used equations from mechanics, electricity, waves, thermodynamics and modern physics. Each entry is presented with a clear bilingual explanation, making it a valuable revision resource for students preparing for A‑Level or equivalent examinations.
物理公式是描述自然规律的简洁语言，概括了可测量量之间的基本关系。本汇编汇集了力学、电学、波、热力学和现代物理中最常用的方程。每个条目都配有清晰的双语解释，是备考 A‑Level 或同等水平考试的学生的宝贵复习资料。
1. Kinematics Equations | 运动学公式
The first equation of motion for constant acceleration relates final velocity to initial velocity, acceleration and time.
v = u + at
匀加速直线运动的第一方程，将末速度与初速度、加速度和时间联系起来：v 是末速度，u 是初速度，a 是恒定加速度，t 是时间。
This equation gives the displacement in terms of initial velocity, acceleration and time.
s = ut + ½at²
位移公式用初速度、加速度和时间表达位移 s：s 是位移，u 是初速度，a 是加速度，t 是时间，½at² 表示加速度引起的附加位移。
When time is not known, the following relation between velocity and displacement is used.
v² = u² + 2as
当时间未知时，使用速度与位移的关系式：v² 等于初速度的平方加上 2as，适用于匀加速直线运动。
The displacement can also be expressed as the product of average velocity and time.
s = ½ (u + v) t
位移还可以用平均速度与时间的乘积表示，即初速与末速的平均值乘以时间。
2. Newton’s Laws and Forces | 牛顿定律与力
Newton’s second law is the foundation of dynamics: the net force on an object equals its mass times its acceleration.
F = m a
牛顿第二定律是动力学的基础，物体受到的合外力等于质量乘以加速度，F 为合力，m 为质量，a 为加速度。
The weight of an object near the Earth’s surface is proportional to its mass.
W = m g
地球表面附近物体的重力等于质量乘以重力加速度 g（约 9.81 m s⁻²），方向竖直向下。
Hooke’s law describes the restoring force of a spring within its elastic limit.
F = k x
胡克定律给出弹簧在弹性限度内的恢复力：F 为恢复力，k 为弹簧劲度系数，x 为形变量，负号表示力与位移方向相反（此处常写作大小形式）。
3. Work, Energy and Power | 功、能和功率
The work done by a constant force is the product of the force, the displacement and the cosine of the angle between them.
W = F s cosθ
恒力所做的功等于力、位移和它们夹角余弦的乘积：W 为功，F 为力，s 为位移，θ 为力与位移的夹角。
Kinetic energy is the energy an object possesses due to its motion.
Ek = ½ m v²
动能是物体由于运动而具有的能量：Ek 等于质量乘以速度平方的一半。
Gravitational potential energy near the Earth’s surface depends on height.
Ep = m g h
地球表面附近的重力势能等于质量、重力加速度和高度的乘积：h 为相对参考点的高度。
Power is the rate of doing work or transferring energy.
P = W / t = F v
功率是做功或能量转移的速率，可以用功除以时间表示，也可表示为力乘以速度。
4. Momentum and Collisions | 动量与碰撞
Momentum is the product of an object’s mass and velocity.
p = m v
动量是物体质量与速度的乘积，是矢量，方向与速度相同。
The impulse experienced by an object equals the change in its momentum.
F Δt = Δp
冲量等于动量的变化量：平均力 F 乘以作用时间 Δt 等于动量的改变量 Δp。
In a closed system, the total momentum before a collision equals the total momentum after.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
在封闭系统中，碰撞前总动量等于碰撞后总动量，这是动量守恒定律的表达式，适用于一切相互作用。
5. Circular Motion and Gravitation | 圆周运动与万有引力
For an object in uniform circular motion, the centripetal acceleration points towards the centre.
a = v² / r = ω² r
匀速圆周运动的向心加速度指向圆心，大小等于线速度平方除以半径，或角速度平方乘以半径。
The centripetal force required to keep an object moving in a circle is given by:
F = m v² / r = m ω² r
维持圆周运动所需的向心力等于质量乘以向心加速度，方向始终指向圆心。
Newton’s law of universal gravitation describes the attractive force between two masses.
F = G M m / r²
牛顿万有引力定律：两质点间的引力与质量乘积成正比，与距离平方成反比，G 为引力常量。
6. Electric Fields and Circuits | 电场与电路
Ohm’s law relates the voltage across a resistor to the current flowing through it.
V = I R
欧姆定律，导体两端电压 V 等于电流 I 与电阻 R 的乘积，适用于恒定电阻的情况。
The resistance of a wire depends on its resistivity, length and cross-sectional area.
R = ρ L / A
导体的电阻与电阻率 ρ、长度 L 成正比，与横截面积 A 成反比。
Electric power dissipated in a resistor can be expressed in three equivalent forms.
P = I V = I² R = V² / R
电功率可用电流与电压的乘积，或电流平方乘电阻，或电压平方除以电阻计算。
For resistors in series, the total resistance is the sum; for parallel, the reciprocals add.
Series: Rtotal = R₁ + R₂ + …
Parallel: 1/Rtotal = 1/R₁ + 1/R₂ + …
串联电阻的总电阻等于各电阻之和；并联电阻的总电阻的倒数等于各电阻倒数之和。
7. Magnetic Fields and Forces | 磁场与磁力
The force on a current-carrying wire in a magnetic field is given by Fleming’s left-hand rule.
F = B I L sinθ
通电导线在磁场中受到的安培力，大小 F = B I L sinθ，其中 B 为磁感应强度，I 为电流，L 为导线长度，θ 为电流与磁场的夹角。
A moving charged particle in a magnetic field experiences a force perpendicular to its velocity.
F = q v B sinθ
运动电荷在磁场中受到的洛伦兹力，大小等于电荷量 q、速度 v、磁感应强度 B 和夹角正弦的乘积。
For a charged particle moving perpendicularly to a uniform magnetic field, the radius of its circular path is:
r = m v / (q B)
当带电粒子垂直射入匀强磁场时，做匀速圆周运动的半径 r 由动量与磁力和电荷的比值决定。
8. Waves and Optics | 波与光学
The wave equation connects wave speed, frequency and wavelength.
v = f λ
波速等于频率与波长的乘积，适用于所有波动形式，如声波、电磁波等。
Snell’s law describes the refraction of light at a boundary between two media.
n₁ sinθ₁ = n₂ sinθ₂
折射定律（斯涅尔定律）：入射角与折射角的正弦之比等于两种介质折射率的反比。
For a diffraction grating, constructive interference occurs at angles satisfying this condition.
d sinθ = n λ
衍射光栅中，当相邻狭缝的光程差为整数倍波长时产生亮条纹，d 为光栅常数，n 为级数。
9. Thermodynamics | 热力学
The amount of heat energy required to change the temperature of a substance is given by its specific heat capacity.
Q = m c Δθ
热量 Q 等于质量 m、比热容 c 和温度变化 Δθ 的乘积，常用于计算加热或冷却过程中的能量转移。
The ideal gas law relates pressure, volume, temperature and the amount of substance.
p V = n R T
理想气体状态方程：压强 p 乘以体积 V 等于物质的量 n、普适气体常量 R 和热力学温度 T 的乘积。
The first law of thermodynamics states that the change in internal energy equals the heat added minus the work done by the system.
ΔU = Q – W
热力学第一定律：系统内能的变化等于吸收的热量减去对外做的功，体现了能量守恒。
10. Quantum and Nuclear Physics | 量子与核物理
The energy of a photon is directly proportional to its frequency.
E = h f
光子能量 E 等于普朗克常数 h 乘以频率 f，也称光子能量方程。
Einstein’s photoelectric equation gives the maximum kinetic energy of emitted electrons.
Ek max = h f – Φ
爱因斯坦光电效应方程：光电子的最大初动能等于光子能量减去金属的逸出功 Φ。
The de Broglie wavelength associates a wave nature with moving particles.
λ = h / p = h / (m v)
德布罗意波长将波动性与粒子动量联系起来，p 为动量，m 为粒子质量，v 为速度。
Mass-energy equivalence is the cornerstone of nuclear processes.
E = m c²
质能方程表明质量 m 与能量 E 可以相互转化，c 为真空中光速，是核反应释放巨大能量的基础。
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