📚 Year 7 Cambridge Physics: Formulae & Theorems Quick Reference | Year 7 Cambridge 物理：公式定理速查手册
This handbook provides a concise collection of essential formulae and theorems for the Year 7 Cambridge physics curriculum. Every definition, equation and principle is presented in a clear bilingual format to support quick revision and deeper understanding. Use it alongside your class notes and practical work to reinforce key concepts.
本手册为 Year 7 剑桥物理课程的核心公式和定理速查提供简明汇编。每个定义、方程和原理都以清晰的双语形式呈现，便于快速复习和深入理解。结合课堂笔记和实验来巩固关键概念。
1. Basic Physical Quantities and Units | 基本物理量与单位
Before applying any formula, we must be comfortable with the quantities we measure and the units we use. The table below lists the most common quantities in Year 7 physics with their SI units and symbols.
在应用任何公式之前，我们必须熟悉我们测量的量及使用的单位。下表列出了 Year 7 物理中最常见的量及其国际单位制和符号。
| Quantity | Symbol | SI Unit | Unit Symbol |
|---|---|---|---|
| length / distance | d, s, x | metre | m |
| mass | m | kilogram | kg |
| time | t | second | s |
| temperature | T, θ | degree Celsius | °C |
| force | F | newton | N |
| energy / work | E, W | joule | J |
| current | I | ampere | A |
| voltage | V | volt | V |
Always check that quantities are expressed in these standard units before substituting into any equation. Inappropriate units are a common source of error.
在代入任何方程之前，务必检查各量已用这些标准单位表示。单位不当是常见的错误来源。
2. Speed, Distance and Time | 速度、距离与时间
Speed tells us how fast an object is moving. It is a scalar quantity that only depends on the total path length and the time taken.
速度告诉我们物体运动的快慢。它是一个标量，只取决于总路径长度和所用的时间。
speed = distance ÷ time or v = d / t
Here, v is the average speed, d is the distance travelled and t is the time taken. You can rearrange this formula to find distance: d = v × t, or time: t = d / v.
此处 v 为平均速度，d 为移动距离，t 为所用时间。你可以变形公式求距离：d = v × t，或求时间：t = d / v。
I unit of speed is metre per second (m/s), but kilometres per hour (km/h) is often used in everyday life.
当运动不是直线时，我们仍使用总距离。如果你绕着 400 m 跑道跑了 50 s，你的平均速度就是 400 m ÷ 50 s = 8 m/s。速度的国际单位是米每秒 (m/s)，但生活中常用千米每小时 (km/h)。
3. Acceleration | 加速度
Acceleration is the rate at which an object's velocity changes. Like velocity, it is a vector, but here we focus on its size when motion is along a straight line.
加速度是物体速度变化的快慢。与速度一样，它是矢量，但此处我们只关注直线运动中加速度的大小。
acceleration = change in velocity ÷ time or a = (v − u) / t
In this formula, u is the initial velocity, v is the final velocity and t is the time taken for the change. A negative acceleration (v < u) means the object is decelerating or slowing down. The unit of acceleration is metre per second squared (m/s²).
该公式中，u 是初速度，v 是末速度，t 是变化所用的时间。负的加速度 (v < u) 表示物体正在减速。加速度的单位是米每二次方秒 (m/s²)。
(25 − 5) ÷ 4 = 5 m/s². Understanding acceleration helps explain how forces change motion.
如果一辆汽车在 4 秒内从 5 m/s 加速到 25 m/s，其加速度为 (25 − 5) ÷ 4 = 5 m/s²。理解加速度有助于解释力如何改变运动。
4. Mass, Weight and Gravity | 质量、重量与引力
Mass and weight are often confused, but they are completely different concepts. Mass is the amount of matter in an object and is measured in kilograms (kg). Weight is the force of gravity acting on that mass.
质量和重量常被混淆，但它们是截然不同的概念。质量是物体所含物质的多少，以千克 (kg) 为单位。重量是作用在该质量上的引力。
weight = mass × gravitational field strength or W = m × g
On Earth, the gravitational field strength g is approximately 9.8 N/kg, but for Year 7 calculations we often use 10 N/kg. This means a 1 kg mass has a weight of about 10 N.
在地球上，引力场强度 g 约为 9.8 N/kg，但在 Year 7 计算中我们常使用 10 N/kg。这意味着质量为 1 kg 的物体，其重量大约为 10 N。
Mass does not change when you go to the Moon, but your weight decreases because the Moon's gravitational field strength is only about 1.6 N/kg. Weight is always measured in newtons (N), never in kilograms.
当你去月球时，质量不会改变，但你的重量会减小，因为月球的引力场强度仅为约 1.6 N/kg。重量始终以牛顿 (N) 为单位，绝不能用千克。
5. Density | 密度
Density describes how tightly packed the particles are in a substance. It links mass and volume and helps us predict whether objects will float or sink.
密度描述物质中粒子排列的紧密程度。它将质量与体积联系起来，帮助我们预测物体是上浮还是下沉。
density = mass ÷ volume or ρ = m / V
The Greek letter ρ (rho) represents density. Mass m is in kilograms (kg) or grams (g), and volume V is in cubic metres (m³) or cubic centimetres (cm³). Common units are kg/m³ and g/cm³.
希腊字母 ρ (rho) 表示密度。质量 m 以千克 (kg) 或克 (g) 为单位，体积 V 以立方米 (m³) 或立方厘米 (cm³) 为单位。常用单位有 kg/m³ 和 g/cm³。
Water has a density of about 1.0 g/cm³. A material with density greater than water will sink, while one with lower density will float. You can determine the density of an irregular solid by measuring its mass and using a displacement can to find its volume.
水的密度约为 1.0 g/cm³。密度大于水的材料会下沉，密度小于水的会上浮。你可以通过测量质量并使用排水法求出体积来确定不规则固体的密度。
6. Stretching and Hooke's Law | 拉伸与胡克定律
When a spring is stretched by a force, the extension increases in a predictable way. Hooke's Law describes this linear relationship for many elastic materials up to their elastic limit.
当弹簧被力拉伸时，伸长量以可预测的方式增加。胡克定律描述了许多弹性材料在弹性限度内的这种线性关系。
force = spring constant × extension or F = k × x
Here, F is the applied force in newtons (N), k is the spring constant (a measure of stiffness) in N/m, and x is the extension (change in length) in metres (m). The law is only valid while the spring returns to its original length when the force is removed.
式中 F 是施加的力 (N)，k 是弹簧常数 (刚度度量)，单位为 N/m，x 是伸长量 (长度变化)，单位为 m。该定律仅在弹簧撤去力后能够恢复原长时才有效。
If the force is too large, the material may reach its elastic limit and become permanently deformed. Hooke's Law then no longer applies. Always record extension, not total length, when drawing extension-force graphs.
如果力过大，材料可能达到弹性极限并发生永久变形，此时胡克定律不再适用。在绘制伸长量-力图像时，始终记录伸长量而非总长度。
7. Balanced and Unbalanced Forces | 平衡力与非平衡力
A force can change an object's shape, speed or direction. Whether the overall effect is zero or not depends on the net force.
力可以改变物体的形状、速度或方向。总效果是否为零取决于合力。
resultant force = sum of all forces in one direction
When forces on an object are balanced, the resultant force is zero. According to Newton's First Law, an object with zero resultant force remains at rest or continues to move at a constant velocity in a straight line.
当物体所受的力平衡时，合力为零。根据牛顿第一定律，合力为零的物体保持静止或沿直线匀速运动。
When forces are unbalanced, the object accelerates in the direction of the resultant force. The size and direction of the resultant force determine how the motion changes. Free-body diagrams are essential tools for identifying all forces and calculating the net force.
当力不平衡时，物体沿合力方向加速。合力的大小和方向决定了运动如何改变。受力图是识别所有力并计算合力的基本工具。
8. Energy Transfers and Conservation | 能量转移与守恒
Energy cannot be created or destroyed; it can only be transferred from one store to another or dissipated. This is the principle of conservation of energy, a cornerstone of physics.
能量既不能创生也不能消灭，只能从一个储存转移或耗散到另一个。这就是能量守恒定律，物理学的基石。
In Year 7, we recognise common energy stores: kinetic, thermal, chemical, gravitational potential, elastic potential and nuclear. Energy is measured in joules (J). When a ball is thrown upwards, kinetic energy is transferred to gravitational potential energy.
在 Year 7，我们识别常见的能量储存：动能、热能、化学能、重力势能、弹性势能和核能。能量以焦耳 (J) 为单位。当球向上抛出时，动能转化为重力势能。
Efficiency describes how much of the input energy is usefully transferred. While we introduce it qualitatively, the formula is efficiency = (useful output energy ÷ total input energy) × 100%. In many systems, some energy is always dissipated as thermal energy to the surroundings.
效率描述输入能量中有多少被有效转移。虽然我们定性引入，但公式为 效率 = (有用输出能量 ÷ 总输入能量) × 100%。在许多系统中，总有一部分能量作为热能散逸到周围环境中。
9. Electrical Circuits | 电路基础
An electric circuit needs a complete loop for charge to flow. Current is the rate of flow of electric charge, measured in amperes (A) with an ammeter connected in series.
电路需要完整的回路才能使电荷流动。电流是电荷流动的速率，单位为安培 (A)，用电流表串联测量。
Voltage (potential difference) is the energy transferred per unit charge and is measured in volts (V) using a voltmeter connected in parallel. A cell or battery provides a 'push' that drives current around the circuit.
电压 (电势差) 是每单位电荷转移的能量，单位为伏特 (V)，用电压表并联测量。电池为回路中的电流提供“推动力”。
is for current to flow. For now, think of it as opposition in the circuit; longer or thinner wires have greater resistance. Although Ohm' later, you can already see the relationship: for a fixed voltage, a larger resistance gives a smaller current.
电阻是衡量电流流动难易程度的量。目前你可以将其想象成电路中的阻碍；导线越长或越细，电阻越大。虽然欧姆定律 (V = I × R) 稍后正式引入，但你已经能看到这一关系：在电压一定时，电阻越大，电流越小。
10. Wave Properties: Frequency, Wavelength and Speed | 波的特性：频率、波长与波速
Waves transfer energy without transferring matter. In Year 7, we explore transverse waves (e.g. light) and longitudinal waves (e.g. sound).
波传递能量而不传递物质。在 Year 7，我们探索横波 (如光) 和纵波 (如声音)。
The key quantities are amplitude (maximum displacement from rest position), wavelength (distance between two identical points on consecutive waves), and frequency (number of complete waves passing a point per second, measured in hertz, Hz).
关键量有振幅 (偏离平衡位置的最大位移)、波长 (相邻波上两个相同点之间的距离) 和频率 (每秒通过某点的完整波数，单位为赫兹 Hz)。
wave speed = frequency × wavelength or v = f × λ
Here, v is wave speed in m/s, f is frequency in Hz, and λ (lambda) is wavelength in m. This equation applies to all waves. In a given medium, if the frequency increases, the wavelength must decrease to keep the wave speed constant.
式中 v 为波速 (m/s)，f 为频率 (Hz)，λ (lambda) 为波长 (m)。此方程适用于所有波。在给定介质中，若频率增大，波长必然减小以保持波速恒定。
Sound waves travel faster in solids than in gases. The wave speed formula helps you calculate one quantity when the other two are known, and it reinforces the link between time, distance and frequency in oscillatory motion.
声波在固体中比在气体中传播更快。波速公式帮助你在已知其中两个量时计算第三个量，并强化了振动运动中时间、距离与频率之间的联系。
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