📚 A-Level Physics Core Formula Summary | A-Level物理核心公式归纳
This article provides a structured summary of the essential formulas required for A-Level Physics. It is organised by topic, with each formula presented in its standard form and accompanied by a brief note on its conditions of use. The aim is to help candidates consolidate their revision and apply equations confidently in examinations.
本文按专题系统梳理 A-Level 物理考试所需的核心公式，每个公式均给出标准形式及适用条件，帮助考生高效复习并在考试中自信运用。
1. Kinematics | 运动学
For motion in a straight line with constant acceleration, the following equations apply. These are often called the SUVAT equations.
对于匀变速直线运动，以下方程成立，通常称为 SUVAT 方程组。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
Here, u is initial velocity, v is final velocity, a is acceleration, t is time, and s is displacement. These equations are only valid when acceleration is constant.
其中 u 为初速度，v 为末速度，a 为加速度，t 为时间，s 为位移。这些方程仅在加速度恒定条件下成立。
Choose a positive direction and keep signs consistent throughout the calculation.
选定正方向后，整个计算过程中符号必须保持一致。
For vertical motion under gravity, a = g ≈ 9.81 m s⁻².
在重力作用下的竖直运动中，a = g ≈ 9.81 m s⁻²。
2. Newton's Laws and Forces | 牛顿定律与力
Newton's second law relates resultant force to mass and acceleration. This is the fundamental equation for dynamics.
牛顿第二定律将合力与质量和加速度联系起来，是动力学的核心方程。
F = ma
For an object of mass m on a horizontal surface, the normal reaction is equal to mg when there is no vertical acceleration. For an object on an inclined plane, the component of weight acting down the slope is mg sin θ.
对于水平面上质量为 m 的物体，若无竖直方向加速度，支持力等于 mg。对于斜面上的物体，重力沿斜面向下的分量为 mg sin θ。
Friction: F ≤ μR, where μ is the coefficient of friction and R is the normal reaction.
摩擦力：F ≤ μR，其中 μ 为摩擦系数，R 为正压力。
Moment of a force: M = Fd, perpendicular distance from the pivot.
力矩：M = Fd，d 为力的作用线到转轴的垂直距离。
3. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object through a distance. The general equation is as follows.
当力使物体移动一段距离时即做功。一般公式如下。
W = Fs cos θ
the direction of motion. When force and displacement are in the same direction, cos θ = 1.
其中 θ 为力的方向与位移方向之间的夹角。当力与位移同向时，cos θ = 1。
Kinetic energy: Eₖ = ½mv²
动能：Eₖ = ½mv²
Gravitational potential energy change: ΔEₚ = mgΔh
重力势能变化：ΔEₚ = mgΔh
Elastic potential energy: Eₑ = ½kx² for a spring obeying Hooke's law.
弹性势能：Eₑ = ½kx²，适用于遵守胡克定律的弹簧。
Power: P = W/t = Fv (for constant force and velocity).
功率：P = W/t = Fv（适用于恒力与恒定速度）。
Efficiency = useful output power / total input power.
效率 = 有用输出功率 / 总输入功率。
4. Momentum | 动量
Momentum is the product of mass and velocity. It is a vector quantity and is conserved in all closed systems.
动量是质量与速度的乘积，是矢量，在一切封闭系统中守恒。
p = mv
Newton's second law can also be written in terms of momentum change, which is the original form of the law.
牛顿第二定律也可以用动量变化率表达，这也是该定律的原始形式。
F = Δp / Δt
For an elastic collision, both momentum and kinetic energy are conserved.
在弹性碰撞中，动量和动能均守恒。
For an inelastic collision, only momentum is conserved; some kinetic energy is transferred to other forms.
在非弹性碰撞中，仅动量守恒，部分动能转化为其他形式的能量。
Impulse: I = FΔt = Δp, equal to the area under a force-time graph.
冲量：I = FΔt = Δp，等于力-时间图像下的面积。
5. Circular Motion | 圆周运动
When an object moves in a circle with angular speed ω, its linear speed v is related to the radius r.
当物体以角速度 ω 做圆周运动时，其线速度 v 与半径 r 的关系如下。
v = ωr
The centripetal acceleration is always directed toward the centre of the circle.
向心加速度始终指向圆心。
a = v²/r = ω²r
F = mv²/r = mω²r
For vertical circular motion, the resultant of weight and tension/normal force provides the centripetal force.
在竖直圆周运动中，重力与张力/支持力的合力提供向心力。
Period T = 2π/ω = 2πr/v.
周期 T = 2π/ω = 2πr/v。
6. Gravitational Fields | 引力场
Newton's law of gravitation states that the force between two point masses is proportional to the product of their masses and inversely proportional to the square of their separation.
牛顿万有引力定律指出，两个质点之间的引力与质量乘积成正比，与距离的平方成反比。
F = Gm₁m₂ / r²
Here, G is the gravitational constant, 6.67 × 10⁻¹¹ N m² kg⁻².
其中 G 为万有引力常量，取值为 6.67 × 10⁻¹¹ N·m²·kg⁻²。
Gravitational field strength: g = F/m = GM/r².
引力场强度：g = F/m = GM/r²。
Gravitational potential: V = −GM/r, where V = 0 at infinity.
引力势：V = −GM/r，无穷远处 V = 0。
Orbital speed of a satellite: v = √GM/r.
卫星轨道速度：v = √GM/r。
Kepler's third law: T² = (4π²/GM) r³.
开普勒第三定律：T² = (4π²/GM) r³。
7. Electric Fields | 电场
Coulomb's law gives the electrostatic force between two point charges.
库仑定律给出了两个点电荷之间的静电力。
F = kQ₁Q₂ / r² = Q₁Q₂ / (4πε₀r²)
where k = 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻², and ε₀ is the permittivity of free space.
其中 k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²·C⁻²，ε₀ 为真空介电常数。
Electric field strength: E = F/q = V/d (uniform field), and E = kQ/r² (radial field).
电场强度：E = F/q = V/d（匀强电场），以及 E = kQ/r²（径向电场）。
Electric potential: V = kQ/r (with V = 0 at infinity).
电势：V = kQ/r（无穷远处 V = 0）。
Work done moving a charge through a potential difference: W = qV.
电荷在电势差间移动所做的功：W = qV。
8. Capacitance | 电容
Capacitance is defined as the charge stored per unit potential difference.
电容定义为储存电荷量与电势差之比。
C = Q/V
Energy stored in a capacitor: U = ½QV = ½CV² = Q²/(2C).
电容器储存的能量：U = ½QV = ½CV² = Q²/(2C)。
For capacitors in parallel: Ctotal = C₁ + C₂ + C₃ + ...
电容器并联：总电容 Ctotal = C₁ + C₂ + C₃ + ...
For capacitors in series: 1/Ctotal = 1/C₁ + 1/C₂ + 1/C₃ + ...
电容器串联：1/Ctotal = 1/C₁ + 1/C₂ + 1/C₃ + ...
Discharge through a resistor: Q = Q₀e−t/RC, V = V₀e−t/RC, I = I₀e−t/RC.
通过电阻放电：Q = Q₀e−t/RC，V = V₀e−t/RC，I = I₀e−t/RC。
Time constant: τ = RC. After one time constant, the charge drops to 37% of its initial value.
时间常数：τ = RC。经过一个时间常数后，电荷降为初始值的 37%。
9. Electric Circuits | 电路
Ohm's law and the power equations form the basis of circuit analysis.
欧姆定律与功率方程是电路分析的基础。
V = IR
P = VI = I²R = V²/R
Resistors in series: Rtotal = R₁ + R₂ + R₃ + ...
电阻串联：总电阻 Rtotal = R₁ + R₂ + R₃ + ...
Resistors in parallel: 1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + ...
电阻并联：1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + ...
Electromotive force (EMF) and internal resistance: ε = I(R + r) = V + Ir.
电动势与内阻：ε = I(R + r) = V + Ir。
Potential divider: Vout = Vin × R₂/(R₁ + R₂).
分压电路：Vout = Vin × R₂/(R₁ + R₂)。
10. Magnetic Fields and Electromagnetism | 磁场与电磁感应
The force on a current-carrying conductor in a magnetic field is given by the following.
载流导体在磁场中所受安培力由下式给出。
F = BIl sin θ
where B is the magnetic flux density, I is the current, l is the length of the conductor, and θ is the angle between the conductor and the magnetic field.
其中 B 为磁通密度，I 为电流，l 为导体长度，θ 为导体与磁场方向的夹角。
Force on a moving charge: F = BQv sin θ.
运动电荷所受洛伦兹力：F = BQv sin θ。
Φ = BA cos θ, where θ is the angle between the normal to the area and the magnetic field.
磁通量：Φ = BA cos θ，其中 θ 为面积法线方向与磁场方向的夹角。
Faraday's law: induced EMF ε = −N ΔΦ/Δt.
法拉第定律：感应电动势 ε = −N ΔΦ/Δt。
Lenz's law determines the direction of the induced current: it opposes the change producing it.
楞次定律决定了感应电流的方向：感应电流总是阻碍引起它的磁通量变化。
For a transformer: Vₛ/Vₚ = Nₛ/Nₚ and VₚIₚ = VₛIₛ (ideal).
对于理想变压器：Vₛ/Vₚ = Nₛ/Nₚ，且 VₚIₚ = VₛIₛ。
11. Thermal Physics and Ideal Gases | 热物理与理想气体
The ideal gas equation combines pressure, volume, temperature and the amount of gas.
理想气体状态方程将压强、体积、温度与气体的量联系起来。
pV = nRT
Alternatively, using Boltzmann's constant k, with N as the number of molecules:
若使用玻尔兹曼常数 k，并用 N 表示分子数，则可写为：
pV = NkT
Internal energy: ΔU = q + W, where q is heat added and W is work done on the system.
内能：ΔU = q + W，其中 q 为系统吸收的热量，W 为外界对系统做的功。
Kinetic energy of gas molecules: average KE = ³⁄₂kT.
气体分子的平均平动动能：平均动能 = ³⁄₂kT。
Root-mean-square speed: crms = √3RT/M = √3kT/m.
方均根速率：crms = √3RT/M = √3kT/m。
12. Oscillations and Waves | 振动与波
Simple harmonic motion (SHM) occurs when acceleration is proportional to displacement and directed toward the equilibrium position.
简谐运动发生时，加速度与位移成正比并指向平衡位置。
a = −ω²x
The displacement of an object in SHM can be expressed as:
简谐运动中的位移可表示为：
x = A cos(ωt) or x = A sin(ωt)
Angular frequency: ω = 2πf = 2π/T.
角频率：ω = 2πf = 2π/T。
Maximum speed: vmax = ωA; maximum acceleration: amax = ω²A.
最大速度：vmax = ωA；最大加速度：amax = ω²A。
For a mass-spring system: T = 2π√m/k.
弹簧振子周期：T = 2π√m/k。
For a simple pendulum: T = 2π√l/g.
单摆周期：T = 2π√l/g。
Wave speed: v = fλ.
波速：v = fλ。
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