📚 KS3 WJEC Physics: Formula & Theorem Quick-Reference Handbook | KS3 WJEC 物理：公式定理速查手册
Welcome to the KS3 WJEC Physics Formula & Theorem Quick-Reference Handbook. This guide brings together the essential equations and principles you need to master for your Key Stage 3 Physics studies under the WJEC curriculum. From motion and forces to energy, electricity and waves, each formula is presented clearly with a brief explanation, its standard form, and a summary of the quantities involved. Every entry is followed by a bilingual quantity table so that you can check symbols and SI units at a glance. Use this handbook as a quick revision aid and a handy reference whenever you tackle physics problems or prepare for exams.
欢迎使用 KS3 WJEC 物理公式定理速查手册。本指南汇集了你在 WJEC 关键阶段 3 物理学习中必须掌握的核心方程和原理。从运动和力到能量、电学与波动，每个公式都通过简明的解释、标准形式以及相关物理量汇总清晰呈现。每个条目后都附有中英对照的物理量表格，方便你一眼核对符号与国际单位。可将本手册用作快速复习工具，在解决物理问题或备考时随手查阅。
1. Speed, Distance and Time | 速度、距离与时间
speed is used, and the standard equation is v = d / t, where v stands for speed, d for distance and t for time. Speed is a scalar quantity, which means it has magnitude but no direction; the SI unit of speed is metres per second (m/s). When a journey has several stages, calculate the speed of each stage separately, or divide the total distance by the total time to find the average speed for the whole journey.
速度衡量物体运动的快慢，它等于通过的总距离除以所用总时间。对于匀速运动我们使用平均速度，标准公式为 v = d / t，其中 v 代表速度，d 代表距离，t 代表时间。速度是标量，只有大小没有方向；速度的国际单位是米/秒（m/s）。当一段行程分为几个阶段时，可以分别计算每一阶段的速度，或者用总距离除以总时间求出全程的平均速度。
v = d / t
The formula uses the following quantities:
该公式使用以下物理量：
| Quantity | Symbol | SI Unit |
|---|---|---|
| 量 | 符号 | 国际单位 |
| Speed (velocity) | v | m/s |
| Distance | d | m |
| Time | t | s |
d = v × t and t = d / v, which are the two forms you will use most often in calculations.
对该公式变形可得 d = v × t 和 t = d / v，这是计算中最常用的两种形式。
2. Acceleration | 加速度
Acceleration tells us how quickly an object' final velocity, u is the initial velocity, and t is the time taken for the change. The unit of acceleration is metres per second squared (m/s²). A positive value means the object is speeding up, a negative value (often called deceleration) means it is slowing down, and a constant value means the velocity changes by the same amount every second.
加速度描述物体速度变化的快慢，它是一个矢量，因此方向的改变同样属于加速。标准公式为 a = (v - u) / t，其中 v 是末速度，u 是初速度，t 是速度变化所用的时间。加速度的单位是米每二次方秒（m/s²）。结果为正值表示物体在加速，为负值（常称为减速度）表示在减速；若数值恒定，说明速度每秒改变相同的量。
a = (v - u) / t
The quantities involved are:
涉及的物理量有：
| Quantity | Symbol | SI Unit |
|---|---|---|
| 量 | 符号 | 国际单位 |
| Final velocity | v | m/s |
| Initial velocity | u | m/s |
| Time | t | s |
| Acceleration | a | m/s² |
On a velocity-time graph the gradient of the line equals the acceleration, and the area under the line equals the distance travelled.
在速度—时间图像上，直线的斜率等于加速度，直线下方的面积等于通过的距离。
3. Newton's Second Law | 牛顿第二定律
Newton' y its acceleration: F = m a. Force is measured in newtons (N), mass in kilograms (kg) and acceleration in m/s². One newton is the resultant force that gives a mass of 1 kg an acceleration of 1 m/s². If the resultant force is zero, the object stays at rest or moves at a constant velocity; if the resultant force increases, the acceleration increases in proportion.
牛顿第二定律描述了力、质量和加速度之间的关系。作用在物体上的合力等于质量乘以加速度：F = m a。力的单位是牛顿（N），质量的单位是千克（kg），加速度的单位是 m/s²。1 牛顿就是使质量为 1 kg 的物体产生 1 m/s² 加速度的合力。如果合力为零，物体保持静止或做匀速直线运动；如果合力增大，加速度也按比例增大。
F = m a
Summary of the quantities:
物理量汇总：
| Quantity | Symbol | SI Unit |
|---|---|---|
| 量 | 符号 | 国际单位 |
| Resultant force | F | N |
| Mass | m | kg |
| Acceleration | a | m/s² |
4. Weight, Mass and Gravity | 重量、质量与重力
ing on that mass and is measured in newtons, so it changes from planet to planet. The equation linking them is W = m g, where W is weight, m is mass and g is the gravitational field strength. On Earth g is about 9.8 N/kg, and in KS3 work it is often rounded to 10 N/kg.
质量是物体所含物质的多少，单位是千克，它在宇宙任何地方都保持不变。重量是重力作用在该质量上的力，单位是牛顿，因此在不同星球上会改变。两者的关系式为 W = m g，其中 W 是重量，m 是质量，g 是重力场强度。地球上的 g 约为 9.8 N/kg，在 KS3 的题目中常取近似值 10 N/kg。
W = m g
The quantities involved are:
涉及的物理量有：
| Quantity | Symbol | SI Unit |
|---|---|---|
| 量 | 符号 | 国际单位 |
| Weight | W | N |
| Mass | m | kg |
| Gravitational field strength | g | N/kg |
A useful check: 1 kg on Earth weighs about 10 N, so a 50 kg student has a weight of roughly 500 N.
一个实用的检验：地球上 1 kg 约重 10 N，所以体重 50 kg 的同学重量约为 500 N。
5. Moments and Pressure | 力矩与压强
ent, F is the force and d is the perpendicular distance from the pivot to the line of action of the force. The unit of moment is the newton metre (N m). For an object to be balanced, the total clockwise moment must equal the total anticlockwise moment, which is the principle of moments.
力矩是力绕支点产生的转动效果，计算公式为 M = F d，其中 M 是力矩，F 是力，d 是从支点到力的作用线的垂直距离。力矩的单位是牛顿米（N m）。物体保持平衡的条件是顺时针力矩总和等于逆时针力矩总和，这就是力矩平衡原理。
M = F d clockwise moment = anticlockwise moment
Pa), and 1 Pa = 1 N/m². A smaller contact area gives a larger pressure, which explains why a sharp knife cuts easily and why snowshoes stop you sinking into soft snow.
压强表示力的集中程度，它等于压力除以受力面积：p = F / A。压强的国际单位是帕斯卡（Pa），1 Pa = 1 N/m²。接触面积越小，压强越大，这解释了为什么锋利的刀容易切割，以及为什么雪地靴能防止人陷入松软的雪中。
p = F / A
| Quantity | Symbol | SI Unit |
|---|---|---|
| 量 | 符号 | 国际单位 |
| Moment | M | N m |
| Force | F | N |
| Perpendicular distance | d | m |
| Pressure | p | Pa (N/m²) |
| Area | A | m² |
6. Work Done and Energy Transfer | 做功与能量传递
joules (J), F is the force in newtons (N) and d is the distance moved in metres (m) in the direction of the force. One joule of work is done when a force of 1 N moves an object 1 m. Work done is really a measure of energy transferred, because energy is neither created nor destroyed but only transferred between stores.
当力使物体沿力的方向移动一段距离时，就说这个力做了功。公式为 W = F d，其中 W 是功，单位是焦耳（J）；F 是力，单位是牛顿（N）；d 是沿力方向移动的距离，单位是米（m）。1 N 的力使物体移动 1 m，所做的功就是 1 J。做功本质上就是能量转移的量度，因为能量既不会凭空产生也不会消失，只会在不同的能量储存之间转移。
W = F d
In KS3 you should be able to describe energy transfers between stores, for example:
在 KS3 阶段，你应当能够描述能量在不同储存之间的转移，例如：
- Chemical store → thermal store (burning fuel) | 化学能储存 → 热能储存（燃烧燃料）
- Gravitational potential store → kinetic store (a falling ball) | 重力势能储存 → 动能储存（下落的球）
- Elastic potential store → kinetic store (a stretched catapult) | 弹性势能储存 → 动能储存（拉紧的弹弓）
- Electrical transfer → light and thermal stores (a lamp) | 电能传输 → 光能储存与热能储存（灯泡）
Energy is measured in joules, and the total energy before and after any transfer remains the same.
能量的单位是焦耳，在任何能量转移前后，能量的总量保持不变。
7. Kinetic Energy, Potential Energy and Efficiency | 动能、势能与效率
hich is why speed limits matter so much in road safety. Gravitational potential energy is the energy stored when an object is raised: Ep = m g h, where h is the height in metres. When an object falls freely, gravitational potential energy is transferred to the kinetic store.
运动物体的动能取决于它的质量和速度：Ek = ½ m v²。这意味着速度加倍，动能变为原来的四倍，这也是道路交通安全中限速如此重要的原因。重力势能是物体被抬高时储存的能量：Ep = m g h，其中 h 是高度，单位是米。当物体自由下落时，重力势能转移为动能储存。
Ek = ½ m v² Ep = m g h
Efficiency compares the useful energy output with the total energy input. It is usually written as a percentage:
效率是比较有用能量输出与总能量输入的量，通常用百分数表示：
efficiency = (useful energy output ÷ total energy input) × 100%
No device is 100% efficient in practice, because some energy is always dissipated to the thermal store of the surroundings, often by friction or by sound. A more efficient device wastes less energy for the same useful output.
实际上没有器件能达到 100% 的效率，因为总有一部分能量通过摩擦或声音等方式耗散到周围环境的热能储存中。对于同样的有用输出，效率越高的器件浪费的能量越少。
| Quantity | Symbol | SI Unit |
|---|---|---|
| 量 | 符号 | 国际单位 |
| Kinetic energy | Ek | J |
| Potential energy | Ep | J |
| Height | h | m |
| Efficiency | η | % (no unit) |
8. Power | 功率
W), E is energy transferred in joules (J) and t is time in seconds (s). One watt equals one joule per second. Power is not the same as energy: a low-power device left running for a long time can transfer more energy than a high-power device used briefly.
功率是能量转移或做功的快慢。公式为 P = E / t，其中 P 是功率，单位是瓦特（W）；E 是转移的能量，单位是焦耳（J）；t 是时间，单位是秒（s）。1 瓦特等于每秒 1 焦耳。功率与能量并不相同：长时间运行的低功率电器，其转移的能量可能比短时间使用的高功率电器更多。
P = E / t
an also be written as P = F d / t, or P = F v when the object moves at a constant speed v.
由于做功 W = F d，功率也可以写成 P = F d / t；当物体以恒定速度 v 运动时，还可以写成 P = F v。
| Quantity | Symbol | SI Unit |
|---|---|---|
| 量 | 符号 | 国际单位 |
| Power | P | W (J/s) |
| Energy transferred | E | J |
| Time | t | s |
9. Density and States of Matter | 密度与物态
ensity in kilograms per cubic metre (kg/m³), m is mass in kilograms (kg) and V is volume in cubic metres (m³). For solids and liquids the particles are packed closely together, so densities are usually high; gases have widely spaced particles and therefore much lower densities. Density is a property of the material itself and does not depend on the size of the sample.
密度是物质单位体积的质量：ρ = m / V，其中 ρ（读作 rho）是密度，单位是千克每立方米（kg/m³）；m 是质量，单位是千克（kg）；V 是体积，单位是立方米（m³）。固体和液体的粒子排列紧密，因此密度通常较大；气体的粒子间距很大，密度就要低得多。密度是材料本身的属性，与样品的大小无关。
ρ = m / V
Water has a density of about 1000 kg/m³, which is why an
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