📚 Year 7 CCEA Physics: Formula & Theorem Quick-Reference Handbook | CCEA 七年级物理：公式定理速查手册
This quick-reference handbook brings together all the essential formulae and theorems you will meet in Year 7 CCEA Physics. Each entry is explained with clear definitions, standard units, and a worked example to help you build confidence when solving problems. Use it to reinforce classwork, prepare for tests, and develop the foundation for Key Stage 3 Science.
这份速查手册汇集了你在 CCEA 七年级物理课程中会接触到的所有核心公式和定理。每一条内容都配有清晰的定义、标准单位和使用示例，帮助你建立解题的信心。你可以用它巩固课堂所学，准备测验，并为 Key Stage 3 科学课程打下扎实的基础。
1. Speed, Distance and Time | 速度、距离与时间
When an object moves, we can describe how fast it travels using the speed formula. Speed is the distance covered in a certain amount of time. In Year 7, we use the average speed equation because objects rarely travel at exactly the same speed for a whole journey.
当物体运动时，我们可以用速度公式来描述它运动的快慢。速度是一定时间内通过的距离。在七年级，我们通常使用平均速度公式，因为物体很少在整个运动过程中保持完全不变的速度。
speed = distance ÷ time
速度 = 距离 ÷ 时间
In symbols: v = d / t (where v = speed, d = distance, t = time). Distance is measured in metres (m), time in seconds (s), so speed is given in metres per second (m/s). For longer journeys we also use kilometres per hour (km/h) or miles per hour (mph).
用符号表示：v = d / t（v 代表速度，d 代表距离，t 代表时间）。距离的单位是米（m），时间的单位是秒（s），因此速度的单位是米每秒（m/s）。在较长的路程中，我们也会用到千米每小时（km/h）或英里每小时（mph）。
Example: A cyclist travels 300 metres in 20 seconds. Her average speed is 300 ÷ 20 = 15 m/s.
示例：一名自行车运动员在 20 秒内行驶了 300 米。她的平均速度是 300 ÷ 20 = 15 米/秒。
- Always check that distance and time are in compatible units before dividing.
- 计算前一定要确认距离和时间的单位是匹配的，然后再相除。
- You can rearrange the formula: distance = speed × time, time = distance ÷ speed.
- 你可以对公式进行变形：距离 = 速度 × 时间，时间 = 距离 ÷ 速度。
2. Weight and Mass | 重量与质量
Mass and weight are often confused in everyday language, but in physics they are quite different. Mass is the amount of matter in an object and is measured in kilograms (kg). Weight is the force of gravity pulling on that mass and is measured in newtons (N).
质量和重量在日常生活中经常被混淆，但在物理学中它们是完全不同的概念。质量是物体所含物质的多少，单位是千克（kg）。重量则是作用在物体上的重力大小，单位是牛顿（N）。
weight = mass × gravitational field strength
重量 = 质量 × 重力场强度
In symbols: W = m g. On Earth, the gravitational field strength (g) is approximately 10 N/kg. This means every 1 kg of mass experiences a weight of about 10 N. The value of g changes slightly on other planets or the Moon.
用符号表示：W = m g。在地球表面，重力场强度（g）大约为 10 N/kg。这意味着每 1 kg 的质量会受到约 10 N 的重力。g 的数值在其他行星或月球上会有所不同。
Example: A school bag has a mass of 6 kg. Its weight on Earth is 6 × 10 = 60 N.
示例：一个书包的质量是 6 kg。它在地球上的重量是 6 × 10 = 60 N。
- Mass does not change with location; weight does.
- 质量不随位置变化而变化，重量则会改变。
- Use a newton meter (spring balance) to measure weight, and a balance to measure mass.
- 测量重量使用弹簧测力计（牛顿计），测量质量则使用天平。
3. Density | 密度
Density tells us how tightly packed the particles in a material are. It links an object’s mass to the volume it occupies. Materials with a high density feel heavy for their size, while low-density materials feel light.
密度反映了物质中粒子排列的紧密程度。它把物体的质量与所占体积联系起来。密度高的材料在相同大小下感觉更重，而密度低的材料则感觉较轻。
density = mass ÷ volume
密度 = 质量 ÷ 体积
In symbols: ρ = m / V (the Greek letter rho, ρ, is used for density). Mass is measured in grams (g) or kilograms (kg), and volume in cubic centimetres (cm³) or cubic metres (m³). Common units for density are g/cm³ and kg/m³.
用符号表示：ρ = m / V（希腊字母 ρ 表示密度）。质量的单位是克（g）或千克（kg），体积的单位是立方厘米（cm³）或立方米（m³）。密度的常用单位是 g/cm³ 和 kg/m³。
Example: A block of wood has a mass of 200 g and a volume of 250 cm³. Its density is 200 ÷ 250 = 0.8 g/cm³. This is less than the density of water (1 g/cm³), so the wood floats.
示例：一块木头的质量是 200 g，体积是 250 cm³。它的密度是 200 ÷ 250 = 0.8 g/cm³。这小于水的密度（1 g/cm³），因此木头会浮在水面上。
- To find the volume of a regular solid, multiply length × width × height.
- 对于形状规则的固体，体积 = 长 × 宽 × 高。
- For irregular solids, use the displacement method with a measuring cylinder.
- 对于形状不规则的固体，可利用排水法用量筒测量体积。
4. Pressure | 压强
Pressure describes how concentrated a force is over an area. A sharp knife cuts easily because the force is concentrated on a very small area, producing a high pressure. Snowshoes stop you sinking into snow by spreading your weight over a large area, reducing pressure.
压强用来描述力在一定面积上的集中程度。锋利的刀容易切割，是因为力集中在很小的面积上，产生了较大的压强。雪鞋通过把人的重量分散到较大的面积上，减小压强，防止陷入雪中。
pressure = force ÷ area
压强 = 压力 ÷ 受力面积
In symbols: P = F / A. Force is measured in newtons (N) and area in square metres (m²). The unit of pressure is the pascal (Pa), where 1 Pa = 1 N/m². Sometimes we also use N/cm² for smaller areas.
用符号表示：P = F / A。力的单位是牛顿（N），面积的单位是平方米（m²）。压强的单位是帕斯卡（Pa），1 Pa = 1 N/m²。在面积较小时，我们有时也会使用 N/cm²。
Example: A force of 40 N acts on an area of 0.5 m². The pressure is 40 ÷ 0.5 = 80 Pa.
示例：一个 40 N 的力作用在 0.5 m² 的面积上，压强为 40 ÷ 0.5 = 80 Pa。
- If the same force is applied over a smaller area, pressure increases.
- 如果同样的力作用在更小的面积上，压强会增大。
- Syringes, drawing pins and hydraulic systems all make use of the pressure principle.
- 注射器、图钉和液压系统都利用了压强原理。
5. Hooke’s Law | 胡克定律
When you stretch a spring by adding weights, it extends. Robert Hooke discovered that up to a certain point called the limit of proportionality, the extension of a spring is directly proportional to the force applied to it. This relationship is known as Hooke’s Law.
当你通过增加砝码拉伸弹簧时，弹簧会伸长。罗伯特·胡克发现，在弹性限度内，弹簧的伸长量与施加的外力成正比。这个规律被称为胡克定律。
force = spring constant × extension
弹力 = 弹簧常数 × 伸长量
In symbols: F = k x (or sometimes F = k e). F is the applied force in newtons (N), x (or e) is the extension in metres (m) or centimetres (cm), and k is the spring constant in N/m. A stiffer spring has a larger k value.
用符号表示：F = k x（有时也用 F = k e）。F 是施加的力，单位牛顿（N）；x（或 e）是伸长量，单位米（m）或厘米（cm）；k 是弹簧常数，单位 N/m。弹簧越硬，k 值越大。
Example: A spring extends by 0.02 m when a force of 4 N is applied. The spring constant k = F ÷ x = 4 ÷ 0.02 = 200 N/m.
示例：一根弹簧在受到 4 N 的拉力时伸长了 0.02 m。弹簧常数 k = F ÷ x = 4 ÷ 0.02 = 200 N/m。
- Hooke’s Law only applies when the spring is not overstretched.
- 胡克定律只在弹簧未被过度拉伸时才成立。
- If you remove the force and the spring returns to its original length, the deformation was elastic.
- 如果撤去外力后弹簧能恢复到原长，这种形变称为弹性形变。
6. Work Done | 做功
In physics, ‘work’ is done when a force moves an object through a distance in the direction of the force. Lifting a book off the floor, pushing a trolley along the hall, and climbing stairs all involve doing work. Work transfers energy from one store to another.
在物理学中，当一个力使物体沿力的方向移动一段距离时，我们就说这个力做了功。把书从地板上捡起、推着购物车沿走廊移动、爬楼梯，这些过程都在做功。做功实现了能量从一个存储到另一个存储的转移。
work done = force × distance
做功 = 力 × 距离
In symbols: W = F d. Work is measured in joules (J), force in newtons (N), and distance in metres (m). One joule is the work done when a force of 1 N moves an object 1 m in the direction of the force.
用符号表示：W = F d。功的单位是焦耳（J），力的单位是牛顿（N），距离的单位是米（m）。当 1 N 的力使物体沿力的方向移动 1 m 时，所做的功就是 1 J。
Example: A girl pushes a box with a steady force of 50 N over a distance of 3 m. The work done is 50 × 3 = 150 J.
示例：一个女孩用 50 N 的恒力将一个箱子推了 3 m 远。她做的功是 50 × 3 = 150 J。
- If the force is not parallel to the movement, only the component in the direction of movement counts.
- 如果力的方向与运动方向不平行，只有沿运动方向的分力才做功。
- Work done is equal to the amount of energy transferred.
- 所做的功等于转移的能量总量。
7. Energy Efficiency | 能量效率
Whenever energy is transferred, some of it always ends up in forms that are not useful – often as heat spreading into the surroundings. Efficiency tells us how good a device is at turning input energy into useful output energy. A more efficient device wastes less energy.
能量在转移过程中，总会有一部分转化为非有用的形式——通常是以热量形式散失到周围环境中。效率用来衡量一个装置将输入能量转化为有用输出能量的程度。效率越高的装置，浪费的能量越少。
efficiency = (useful energy output ÷ total energy input) × 100%
效率 = （有用输出能量 ÷ 总输入能量）× 100%
Efficiency can also be calculated using power: efficiency = (useful power output ÷ total power input). The result is given as a percentage. No real device can ever be 100% efficient because of friction, air resistance and electrical heating.
效率也可以用功率来计算：效率 = （有用输出功率 ÷ 总输入功率）。计算结果以百分比表示。由于摩擦、空气阻力和电热效应的存在，任何真实装置的效率都不可能达到 100%。
Example: A light bulb takes in 100 J of electrical energy and gives out 15 J of light energy. Efficiency = (15 ÷ 100) × 100% = 15%.
示例：一个灯泡获得 100 J 的电能，发出 15 J 的光能。效率 = （15 ÷ 100）× 100% = 15%。
- Wasted energy is not destroyed; it is transferred into the thermal store of the surroundings.
- 浪费掉的能量并没有消失，而是转移到周围环境的热存储中。
- LED bulbs are more efficient than filament bulbs because a higher proportion of input energy becomes light.
- LED 灯泡比白炽灯效率更高，因为输入能量转化为光的比例更大。
8. The Law of Reflection | 反射定律
When a ray of light bounces off a smooth surface such as a plane mirror, it follows a simple but very important rule. The law of reflection allows us to predict the path of the reflected ray and is the principle behind periscopes, kaleidoscopes and many optical technologies.
当一束光线在平面镜这样的光滑表面发生反射时，它遵从一条简单却非常重要的规律。反射定律使我们能够预测反射光线的路径，它也是潜望镜、万花筒以及许多光学技术背后的原理。
angle of incidence = angle of reflection
入射角 = 反射角
In symbols: i = r. Both angles are measured from the normal – an imaginary line drawn perpendicular (at 90°) to the mirror surface at the point where the ray hits. The incident ray, the reflected ray and the normal all lie in the same flat plane.
用符号表示：i = r。这两个角都是从法线开始测量的。法线是在光线入射点处垂直于镜面的一条假想线。入射光线、反射光线和法线都处在同一个平面内。
Example: If a light ray hits a plane mirror with an angle of incidence of 30°, it will reflect off at exactly 30° from the normal on the other side.
示例：如果一束光以 30° 的入射角射向平面镜，它将以与法线成 30° 的反射角从另一侧反射出去。
- No matter how the mirror is tilted, the angles are always equal.
- 无论镜子如何倾斜，这两个角始终相等。
- Rough surfaces scatter light in many directions because the normal points in different ways at each point – this is diffuse reflection.
- 粗糙表面上的法线方向各异，导致光线向四面八方散射，这就形成了漫反射。
9. Conservation of Energy | 能量守恒定律
Energy can be stored in different ways and can be transferred from one store to another, but it can never be created or destroyed. This fundamental idea is called the principle of conservation of energy and it governs all physical and chemical processes.
能量可以以不同的形式储存起来，也可以从一个储存转移到另一个储存，但它永远不会凭空产生或消失。这一基本概念被称为能量守恒定律，它支配着所有物理和化学过程。
total energy before a transfer = total energy after a transfer
转移前的总能量 = 转移后的总能量
In Year 7, energy stores include kinetic, gravitational potential, elastic, thermal, chemical, and nuclear. When a ball is kicked, energy moves from the chemical store of the body to the kinetic store of the ball and the thermal store of the surroundings. The total amount of energy stays constant.
在七年级，能量储存包括动能、重力势能、弹性势能、内能（热）、化学能和核能。当足球被踢出时，能量从人体的化学储存转移到球的动能储存和周围环境的热储存中。能量的总量始终保持不变。
Example: A pendulum swinging back and forth constantly transforms energy between gravitational potential and kinetic forms. At the highest points energy is all gravitational potential; at the lowest point it is all kinetic. Ignoring air resistance, the total energy remains the same.
示例：一个来回摆动的钟摆不断在重力势能和动能之间转化。在最高点，能量全部为重力势能；在最低点，能量全部为动能。忽略空气阻力，总能量保持不变。
- ‘Lost’ energy is really energy transferred to stores that are less useful, such as thermal energy spreading into the surroundings.
- 所谓“丢失”的能量，实际上是转移到了用处较小的储存，比如散失到周围环境中的热能。
- Conservation of energy helps us understand why perpetual motion machines are impossible.
- 能量守恒定律帮助我们理解为什么永动机不可能实现。
10. Balanced and Unbalanced Forces | 平衡力与非平衡力
Forces acting on an object can either cancel each other out or combine to produce a change in motion. This is not a single formula but a theorem that builds on Newton’s First Law of Motion. If the forces on an object are balanced, the object’s motion does not change; if they are unbalanced, the object accelerates.
作用在物体上的力要么相互抵消，要么合在一起引起运动状态的改变。这虽然不是一个单独的公式，却是一条建立在牛顿第一运动定律基础上的重要原理。如果作用在物体上的力是平衡的，物体的运动状态保持不变；如果力不平衡，物体就会加速。
balanced forces → no change in speed or direction
平衡力 → 速度或方向不改变
unbalanced forces → acceleration (speeding up, slowing down or changing direction)
非平衡力 → 加速（加快、减慢或改变方向）
We represent forces with arrows in free-body diagrams. The length of the arrow shows the size (magnitude) of the force, and the direction of the arrow shows the direction of the force. If the arrows pointing left are exactly as long as those pointing right, the horizontal forces are balanced.
我们用力图（受力分析图）中的箭头来表示力。箭头的长度表示力的大小，箭头的方向表示力的方向。如果向左的箭头和向右的箭头长度完全相同，那么水平方向上的力就是平衡的。
Example: A book resting on a table has its weight pulling downwards and the table’s normal reaction force pushing upwards. These two forces are equal in size and opposite in direction, so the forces are balanced and the book stays still.
示例：一本放在桌子上的书受到竖直向下的重力和桌子竖直向上的支持力。这两个力大小相等、方向相反，因此力是平衡的，书保持静止。
- When a car travels at a steady speed, the driving force and the total resistive forces (air resistance and friction) are balanced.
- 当汽车匀速行驶时，驱动力与总阻力（空气阻力和摩擦力）达到平衡。
- A skydiver initially accelerates because weight is greater than air resistance, but eventually reaches terminal velocity when the forces balance.
- 跳伞者在初始阶段因重力大于空气阻力而加速，但当两力平衡时，最终会达到终端速度。
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