A-Level Physics: Core Formulas and Applications | A-Level物理：核心公式梳理与运用

📚 A-Level Physics: Core Formulas and Applications | A-Level物理：核心公式梳理与运用

For A-Level physics students, mastering the key formulas is not about memorising isolated equations – it is about understanding how they connect to physical concepts and knowing when to apply them. This guide groups the most frequently tested formulas by topic, explains their meaning, and highlights common pitfalls.

对于A-Level物理学生来说，掌握核心公式并非孤立地记忆方程，而是要理解它们与物理概念的关联，并知道何时运用。本指南按主题将最常考公式分组，解释其含义，并指出常见易错点。

1. Kinematics: Motion with Constant Acceleration | 运动学：匀加速运动

The equations of motion (often called SUVAT equations) describe objects moving in a straight line with constant acceleration. The symbols are: s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time.

运动学方程（常称为SUVAT方程）描述物体在直线上做匀加速运动的情况。符号含义：s = 位移，u = 初速度，v = 末速度，a = 加速度，t = 时间。

v = u + at

s = ut + ½at²

v² = u² + 2as

s = ½(u + v)t

These four equations are only valid when acceleration is constant. A common mistake is using them for projectiles without checking whether air resistance is ignored. For vertical motion, take upward as positive and set a = -g.

这四个方程仅在加速度恒定条件下成立。一个常见错误是忽略空气阻力时将它们用于抛体运动。对于竖直运动，取向上为正，令 a = -g。

Always define a positive direction before writing equations.
Convert units to base SI (e.g. km/h to m/s) first.
When an object stops, v = 0; when it starts from rest, u = 0.

列出方程前先规定正方向。
先将单位转换为国际基本单位（如从km/h换算为m/s）。
物体停止时 v = 0；从静止出发时 u = 0。

2. Dynamics: Newton’s Laws and Momentum | 动力学：牛顿定律与动量

Newton’s second law is often written as F = ma, but its more general form involves momentum: the resultant force equals the rate of change of momentum.

牛顿第二定律常写作 F = ma，但其更一般的形式涉及动量：合外力等于动量变化率。

F = Δp / Δt

For a constant mass, this simplifies to F = ma. Momentum is defined as p = mv, and the impulse-momentum theorem states that impulse = change in momentum, i.e. Ft = Δp.

当质量不变时，该式化简为 F = ma。动量定义为 p = mv，冲量–动量定理表明：冲量 = 动量变化量，即 Ft = Δp。

In collisions, total momentum is conserved if no external resultant force acts. You must use the vector nature of momentum: assign positive and negative signs before adding.

在碰撞中，若没有合外力作用，总动量守恒。你必须注意动量的矢量性：相加前先规定正负方向。

Collision types | 碰撞类型
Type 类型	Kinetic energy 动能
Elastic 弹性	Conserved 守恒
Inelastic 非弹性	Not conserved (some lost as heat/sound) 不守恒（部分转化为热/声）

3. Work, Energy and Power | 功、能与功率

Work is done when a force moves an object through a displacement in the direction of the force. The formula is:

当力使物体沿力的方向发生位移时，力做了功。公式为：

W = Fs cos θ

Here θ is the angle between the force and displacement. If the force is perpendicular to motion, work done is zero – for example, the tension in a string for a horizontal circular motion does no work.

其中θ是力与位移之间的夹角。若力与运动方向垂直，则做功为零——例如水平圆周运动中绳的拉力不做功。

Kinetic energy is Eₖ = ½mv². Gravitational potential energy near the Earth’s surface is Eₚ = mgh. The principle of conservation of energy states that energy cannot be created or destroyed, only transformed.

动能为 Eₖ = ½mv²。地球表面附近的重力势能为 Eₚ = mgh。能量守恒定律指出：能量既不能创生也不能消失，只能转化。

Power is the rate of doing work or transferring energy:

功率是做功或能量转化的速率：

P = W / t = Fv

For a vehicle moving at constant velocity, the driving force must balance resistive forces, so P = Fv often gives useful results.

对于匀速行驶的车辆，驱动力与阻力平衡，因此 P = Fv 常可得出有用结果。

4. Circular Motion and Gravitation | 圆周运动与万有引力

For uniform circular motion, speed is constant but velocity changes direction, so there is a centripetal acceleration directed towards the centre. The key formulas are:

对于匀速圆周运动，速率不变但速度方向改变，因此存在指向圆心的向心加速度。关键公式为：

a = v² / r = ω²r

F = mv² / r = mω²r

The angular speed ω is connected to the period T and frequency f by:

角速度ω与周期T、频率f的关系为：

ω = 2π / T = 2πf

Newton’s law of gravitation gives the force between two point masses:

牛顿万有引力定律给出两个质点之间的引力：

F = GMm / r²

For an orbiting satellite, the gravitational force provides the centripetal force. Equating GMm/r² = mv²/r leads to v = √(GM/r). Thus orbital speed decreases with increasing radius.

对于绕行卫星，万有引力提供向心力。由 GMm/r² = mv²/r 可得 v = √(GM/r)。因此轨道半径越大，轨道速度越小。

5. Simple Harmonic Motion | 简谐运动

An object performs simple harmonic motion (SHM) when its acceleration is proportional to its displacement from equilibrium and directed towards equilibrium. The defining equation is:

当物体的加速度与对其平衡位置的位移成正比且始终指向平衡位置时，物体做简谐运动（SHM）。其定义方程为：

a = -ω²x

The displacement of an object in SHM can be described by x = A cos(ωt) or x = A sin(ωt), where A is amplitude and ω is angular frequency. The period for a mass–spring system is:

简谐运动物体的位移可表示为 x = A cos(ωt) 或 x = A sin(ωt)，其中A为振幅，ω为角频率。弹簧–质量系统的周期为：

T = 2π√(m/k)

For a simple pendulum with small angles, the period is:

对于小角度摆动的单摆，周期为：

T = 2π√(L/g)

Velocity in SHM is given by v = ±ω√(A² – x²). Maximum speed occurs at equilibrium where x = 0; the maximum acceleration occurs at the extremes where x = ±A.

简谐运动的速度为 v = ±ω√(A² – x²)。最大速度出现在平衡位置 x = 0 处；最大加速度出现在端点 x = ±A 处。

6. Wave Motion: Superposition and Standing Waves | 波动：叠加与驻波

All waves satisfy the fundamental wave equation:

所有波都满足基本波方程：

v = fλ

Phase difference and path difference are related by the fact that one complete wavelength corresponds to a phase difference of 2π radians. For two sources with the same frequency, constructive interference occurs when the path difference is nλ (n = 0, 1, 2, …), and destructive interference when it is (n + ½)λ.

相位差与路程差的关系基于一个完整波长对应2π弧度相位差。对于频率相同的两列波，当路程差为 nλ（n = 0, 1, 2, …）时发生相长干涉；当路程差为 (n + ½)λ 时发生相消干涉。

For a string fixed at both ends, standing waves form with nodes at the ends. The allowed wavelengths are λₙ = 2L/n, where n is the harmonic number (1 for fundamental). The frequency is then:

对于两端固定的弦，驻波在两端形成波节。允许的波长为 λₙ = 2L/n，其中n为谐波次数（n = 1对应基频）。频率为：

fₙ = nv / (2L)

For an open pipe, both ends are antinodes and the same formula applies. For a closed pipe (one end closed), only odd harmonics exist: fₙ = nv / (4L) with n = 1, 3, 5, …

对于两端开口的管，两端均为波腹，适用相同公式。对于一端封闭的管（闭管），只存在奇次谐波：fₙ = nv / (4L)，其中 n = 1, 3, 5, …

7. Electricity: Ohm’s Law and Circuits | 电学：欧姆定律与电路

Electric current is the rate of flow of charge:

电流是电荷流动的速率：

I = ΔQ / Δt

Ohm’s law states that the potential difference across a conductor is proportional to the current through it, provided physical conditions (temperature, etc.) remain constant:

欧姆定律指出，在物理条件（如温度等）保持不变时，导体两端的电势差与通过它的电流成正比：

V = IR

Resistors in series add directly: R_total = R₁ + R₂ + … For resistors in parallel, the reciprocal rule applies:

串联电阻直接相加：R_total = R₁ + R₂ + … 对于并联电阻，使用倒数规则：

1/R_total = 1/R₁ + 1/R₂ + …

Electrical power can be expressed in several equivalent forms:

电功率有多种等价表达式：

P = VI = I²R = V²/R

For a cell with electromotive force (emf) ε and internal resistance r, the terminal potential difference V when a current I flows is:

对于电动势为ε、内阻为r的电池，当通过电流I时，路端电压V为：

V = ε – Ir

Maximum power transfer to an external resistor occurs when the external resistance equals the internal resistance (R = r).

当外电阻等于内阻（R = r）时，外电路获得最大功率。

8. Electric and Magnetic Fields | 电场与磁场

The force on a charge in a uniform electric field is F = qE, where E is the electric field strength. Field strength between parallel plates is E = V/d, where V is the potential difference and d is the plate separation. The potential energy of a charge at a point is U = qV.

均匀电场中电荷受力为 F = qE，其中E为电场强度。平行板之间的场强为 E = V/d，其中V为电势差，d为板间距。电荷在某点的电势能为 U = qV。

In a uniform magnetic field, the force on a moving charge is:

在均匀磁场中，运动电荷受到的力为：

F = Bqv sin θ

When the charge moves perpendicular to the field (θ = 90°), the force is maximum and acts as a centripetal force, causing circular motion. Therefore:

当电荷垂直于磁场方向运动（θ = 90°）时，力最大且充当向心力，使电荷做圆周运动。因此：

Bqv = mv²/r ⇒ r = mv/(Bq)

The force on a current-carrying conductor in a magnetic field is:

磁场中载流导线所受的力为：

F = BIL sin θ

Magnetic flux and Faraday’s law are crucial for electromagnetic induction. The induced emf is equal to the rate of change of magnetic flux linkage:

磁通量与法拉第定律对电磁感应至关重要。感应电动势等于磁链的变化率：

ε = -N ΔΦ / Δt

Here N is the number of turns, Φ is the flux per turn, and the negative sign represents Lenz’s law.

其中N为线圈匝数，Φ为每匝磁通量，负号代表楞次定律。

9. Thermal Physics: Ideal Gases and Internal Energy | 热学：理想气体与内能

The ideal gas equation links pressure, volume, temperature and number of moles:

理想气体方程联系了压强、体积、温度与摩尔数：

pV = nRT

In terms of the Boltzmann constant k, using the number of molecules N, it becomes:

若使用玻尔兹曼常数k和分子数N，则该式变为：

pV = NkT

The temperature T must be in kelvin. Convert from Celsius by using T(K) = θ(°C) + 273.15. For a monatomic ideal gas, the average translational kinetic energy of a molecule is:

温度T必须用开尔文。由摄氏温度θ换算：T(K) = θ(°C) + 273.15。对于单原子理想气体，分子的平均平动动能为：

½m⟨c²⟩ = (3/2)kT

This shows that average kinetic energy is proportional to absolute temperature. The root-mean-square speed is then c_rms = √(3kT/m).

这说明平均动能与绝对温度成正比。均方根速度为 c_rms = √(3kT/m)。

Internal energy of an ideal gas is the sum of the random kinetic energies of its molecules. For a monatomic gas, U = (3/2)NkT = (3/2)nRT.

理想气体的内能是其分子无规则动能之和。对于单原子气体，U = (3/2)NkT = (3/2)nRT。

10. Radioactive Decay and Nuclear Physics | 放射性衰变与核物理

Radioactive decay is a random process described by:

放射性衰变是一个随机过程，描述为：

N = N₀ e⁻λt

where N is the number of undecayed nuclei, N₀ is the initial number, λ is the decay constant, and t is time. The activity A = λN, and the decay constant is related to the half-life T₁/₂ by:

其中N为未衰变核数，N₀为初始核数，λ为衰变常数，t为时间。活度 A = λN，衰变常数与半衰期 T₁/₂ 的关系为：

λ = ln 2 / T₁/₂

Mass–energy equivalence is given by Einstein’s famous equation:

质能等价由爱因斯坦著名方程给出：

ΔE = Δmc²

In nuclear reactions, the mass defect (difference between total initial mass and total final mass) corresponds to the energy released. Always use the mass difference in kilograms and c = 3.00 × 10⁸ m/s.

在核反应中，质量亏损（初始总质量与末态总质量之差）对应释放的能量。必须使用以千克为单位的质量差，并取 c = 3.00 × 10⁸ m/s。

11. Quantum Physics: Photons and Electrons | 量子物理：光子与电子

The energy of a photon is proportional to its frequency:

光子的能量与其频率成正比：

E = hf = hc/λ

where h = 6.63 × 10⁻³⁴ J·s is the Planck constant. The photoelectric effect equation is:

其中h = 6.63 × 10⁻³⁴ J·s 为普朗克常量。光电效应方程为：

hf = Φ + Eₖ(max)

Here Φ is the work function (minimum energy to remove an electron) and Eₖ(max) is the maximum kinetic energy of emitted electrons. The threshold frequency f₀ = Φ/h.

其中Φ为逸出功（移出电子所需的最小能量），Eₖ(max)为发射电子的最大动能。极限频率 f₀ = Φ/h。

The de Broglie wavelength of a particle with momentum p is:

动量为p的粒子的德布罗意波长为：

λ = h/p

For an electron accelerated through a potential difference V, its kinetic energy is eV, so p = √(2meV), leading to λ = h/√(2meV).

对于经电压V加速的电子，其动能为 eV，因此 p = √(2meV)，从而 λ = h/√(2meV)。

12. Final Tips for Formula Application | 公式应用最终建议

Do not treat this list as a substitute for understanding the derivation. Examiners often test whether you know the conditions under which a formula applies. For example, F = ma is valid for constant mass systems; pV = nRT assumes an ideal gas; SUVAT equations require constant acceleration.

不要将这份清单视为理解推导过程的替代品。考官经常测试你是否知道公式适用的条件。例如，F = ma 适用于质量恒定的系统；pV = nRT 假设理想气体；SUVAT方程要求匀加速。

Write down the known quantities and identify the unknown before choosing a formula.
Check units – convert to SI first, especially for eV, km/h, g/cm³.
Use vector signs explicitly for velocity, momentum and acceleration.
Always include a short justification for why a formula applies, not just the algebra.

先写下已知量并确定未知量，再选择公式。
检查单位——先转换为国际单位，尤其是eV、km/h、g/cm³。
对速度、动量、加速度明确标注矢量正负号。
不仅要写出代数过程，还要简要说明公式为何适用。

By linking each formula to its physical situation and practising past-paper questions, you will develop the judgement needed to score full marks in A-Level physics exams.

将每个公式与物理情境联系起来，并练习历年真题，你将培养出在A-Level物理考试中拿到满分所需的判断力。

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A-Level Physics: Core Formulas and Applications | A-Level物理：核心公式梳理与运用