GCSE Physics: Formula Summary Handbook | GCSE 物理：公式汇总手册

📚 GCSE Physics: Formula Summary Handbook | GCSE 物理：公式汇总手册

Welcome to the GCSE Physics Formula Summary Handbook. This guide brings together the key equations you need to master for your exam – from speed and acceleration to electrical power and transformers. Each formula is presented with a concise explanation of when and how to use it, followed by a Chinese translation to support bilingual learners. Keep this handbook handy for revision and problem-solving practice.

欢迎使用 GCSE 物理公式汇总手册。本手册汇集了考试要求掌握的核心公式，涵盖速度、加速度、电功率、变压器等主题。每个公式都附有简明使用说明及中文翻译，便于双语学习者查阅。请将本手册用于复习与解题训练。

1. Motion and Kinematics | 运动学

Average speed is the total distance travelled divided by the time taken. Use s for distance and t for time.

平均速率等于移动的总距离除以所用时间。用 s 表示距离，t 表示时间。

v = s / t

Acceleration is the rate of change of velocity. It can be calculated from the change in velocity (final v minus initial u) over the time interval t.

加速度是速度的变化率。可由速度变化量（末速度 v 减初速度 u）除以时间间隔 t 求得。

a = (v − u) / t

For uniform acceleration, the following SUVAT equations link displacement s, initial velocity u, final velocity v, acceleration a and time t.

对匀加速运动，下列 SUVAT 方程联系位移 s、初速度 u、末速度 v、加速度 a 和时间 t。

v = u + a t

s = u t + ½ a t²

v² = u² + 2 a s

2. Forces and Newton’s Second Law | 力与牛顿第二定律

Newton’s second law states that the resultant force on an object is equal to its mass multiplied by its acceleration.

牛顿第二定律指出，作用在物体上的合力等于物体质量乘以其加速度。

F = m a

Weight is the force of gravity on a mass. It depends on the gravitational field strength g (≈ 9.8 N/kg on Earth).

重力是作用在物体上的引力，大小取决于引力场强 g（地球上约为 9.8 N/kg）。

W = m g

In many problems you will resolve forces or use F = m a to find unknown quantities. Always draw a free‑body diagram first.

在许多题目中，需要分解力或应用 F = m a 求未知量。务必先画出受力分析图。

3. Work, Energy and Power | 功、能与功率

Work done by a constant force is the product of the force and the distance moved in the direction of the force.

恒力做的功等于力与沿力方向移动距离的乘积。

W = F d

Gravitational potential energy gained (or lost) when an object is raised (or lowered) through a height h.

物体在竖直方向上移动高度 h 时，增加（或减少）的重力势能。

Eₚ = m g h

Kinetic energy of a moving object depends on its mass and speed. The formula is:

运动物体的动能取决于其质量和速率。

Eₖ = ½ m v²

Power is the rate of doing work or transferring energy.

功率是做功或能量转换的速率。

P = W / t

P = ΔE / t

Efficiency compares useful output energy to total input energy, often expressed as a percentage.

效率对比有用输出能量与总输入能量，常用百分比表示。

η = (useful output / total input) × 100%

4. Momentum | 动量

Momentum is the product of mass and velocity. It is a vector quantity.

动量是质量与速度的乘积，为矢量。

p = m v

The impulse experienced by an object equals the change in momentum. Impulse is also force × time.

物体受到的冲量等于其动量的变化量，冲量也等于力 × 时间。

F t = Δ p = m (v − u)

In a closed system, total momentum before a collision equals total momentum after (conservation of momentum).

在封闭系统中，碰撞前的总动量等于碰撞后的总动量（动量守恒）。

5. Density, Pressure and Moments | 密度、压强与力矩

Density measures how much mass is contained in a given volume.

密度表示单位体积所含质量的大小。

ρ = m / V

Pressure is the force acting per unit area. The unit is pascal (Pa), equivalent to N/m².

压强是单位面积上受到的压力，单位为帕斯卡 (Pa)，即 N/m²。

p = F / A

The moment of a force (turning effect) about a pivot equals force × perpendicular distance from the pivot.

力对支点的力矩（转动效应）等于力 × 支点到力作用线的垂直距离。

M = F × d

For an object in equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.

物体处于平衡状态时，顺时针力矩之和等于逆时针力矩之和。

6. Electricity: Ohm’s Law and Circuit Rules | 电学：欧姆定律与电路法则

Ohm’s law relates voltage (V), current (I) and resistance (R) at constant temperature.

欧姆定律描述在温度不变时电压 (V)、电流 (I) 和电阻 (R) 的关系。

V = I R

In a series circuit:

在串联电路中：

The current is the same at all points: I = I₁ = I₂

各处电流相等：I = I₁ = I₂
The total voltage is shared: Vₜ = V₁ + V₂

总电压等于各部分电压之和：Vₜ = V₁ + V₂
Total resistance adds up: Rₜ = R₁ + R₂ + …

总电阻为各电阻之和：Rₜ = R₁ + R₂ + …

In a parallel circuit:

在并联电路中：

The total current splits: Iₜ = I₁ + I₂

总电流在各个支路分配：Iₜ = I₁ + I₂
The voltage across each branch is the same: V = V₁ = V₂

各支路两端电压相等：V = V₁ = V₂
The total resistance is found from: 1 / Rₜ = 1 / R₁ + 1 / R₂

总电阻的倒数等于各电阻倒数之和：1 / Rₜ = 1 / R₁ + 1 / R₂

7. Electricity: Power and Energy | 电功率与电能

Electrical power is the rate of electrical energy transfer. It can be expressed in three useful forms using Ohm’s law.

电功率是电能转换的速率，结合欧姆定律可表示为三种形式。

P = I V

P = I² R

P = V² / R

Electrical energy transferred in a circuit over time t is given by:

电路中在时间 t 内消耗的电能为：

E = I V t

When using the energy formula, remember to use consistent units: energy in joules (J), power in watts (W), time in seconds (s).

使用能量公式时，务必保持单位统一：能量用焦耳 (J)，功率用瓦特 (W)，时间用秒 (s)。

8. Waves: Speed, Frequency and Wavelength | 波动：波速、频率与波长

The wave equation links wave speed v, frequency f and wavelength λ. It applies to all types of waves including sound and light.

波速公式关联波速 v、频率 f 和波长 λ，适用于声波、光波等所有波。

v = f λ

Frequency is measured in hertz (Hz); wavelength is typically in metres (m). For electromagnetic waves, v is the speed of light c (3.0 × 10⁸ m/s in vacuum).

频率的单位是赫兹 (Hz)，波长通常用米 (m)。对于电磁波，v 为真空中的光速 c = 3.0 × 10⁸ m/s。

9. Thermal Physics: Specific Heat Capacity and Latent Heat | 热学：比热容与潜热

When an object is heated and its temperature changes, the thermal energy transferred depends on mass, specific heat capacity and temperature rise.

物体温度变化时吸收的热量与质量、比热容及温度变化量有关。

ΔQ = m c Δθ

During a change of state (melting or boiling), the temperature remains constant and energy is used to break bonds. The energy required is given by the specific latent heat L.

在物态变化（熔化或沸腾）过程中，温度保持不变，能量用于打破分子间键结。所需能量由比潜热 L 给出。

Q = m L

Use L_f for latent heat of fusion (melting) and L_v for latent heat of vaporisation (boiling). Both are given in J/kg.

熔化潜热用 L_f 表示，汽化潜热用 L_v 表示，单位均为 J/kg。

10. Electromagnetism and Transformers | 电磁学与变压器

A transformer changes the voltage of an alternating current. For an ideal transformer (100% efficiency), the ratio of voltages equals the ratio of turns on the coils.

变压器用于改变交流电压。对理想变压器（效率100%），电压比等于线圈匝数比。

V₁ / V₂ = N₁ / N₂

Since input power ≈ output power, we can also relate currents and turns:

由于输入功率约等于输出功率，可得电流与匝数的关系：

I₁ / I₂ = V₂ / V₁ = N₂ / N₁

Step‑up transformers have more turns on the secondary coil (N₂ > N₁) and step‑down transformers have fewer secondary turns (N₂ < N₁).

升压变压器次级线圈匝数较多 (N₂ > N₁)，降压变压器次级匝数较少 (N₂ < N₁)。

11. Radioactivity and Half‑life | 放射性衰变与半衰期

Activity of a radioactive source is the number of decays per second, measured in becquerel (Bq).

放射源的活度是每秒衰变次数，单位为贝克勒尔 (Bq)。

A = − ΔN / Δt

Half‑life is the time taken for the activity (or number of radioactive nuclei) to fall to half its original value. No universal algebraic formula is required, but you can use the half‑life to calculate decay after a number n of half‑lives:

半衰期是指活度（或放射性核素数目）降至初始值一半所需的时间。没有统一的代数公式，但可利用半衰期个数 n 计算衰变后的剩余量：

remaining activity = initial activity × (½)ⁿ

Carefully read the time intervals and number of half‑lives from a decay graph to answer exam questions.

解题时需准确从衰变图中读出时间间隔和半衰期个数。

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GCSE Physics: Formula Summary Handbook | GCSE 物理：公式汇总手册