📚 Year 7 CIE Physics Formula & Theorem Quick Reference | Year 7 CIE 物理：公式定理速查手册
This quick reference handbook is designed for Year 7 students following the CIE Physics curriculum. It collects all the essential formulas, laws, and principles you need to memorise and apply, from motion and forces to energy, waves, and electricity. Use it to check your understanding before class tests and to build a solid foundation for the years ahead.
这本速查手册专为学习 CIE 物理课程的 Year 7 学生设计。它汇集了你需要记忆和应用的所有基本公式、定律和原理，涵盖从运动和力到能量、波和电学的全部内容。你可以在课堂测验前用它来检查自己的理解，并为未来几年的学习打下坚实基础。
1. Physical Quantities and SI Units | 物理量与国际单位制
Length is measured in metres (m), mass in kilograms (kg), time in seconds (s), electric current in amperes (A), and temperature in Kelvin (K) or degrees Celsius (°C). Every measurement must include a numerical value and its unit.
长度的单位是米 (m)，质量的单位是千克 (kg)，时间的单位是秒 (s)，电流的单位是安培 (A)，温度的单位是开尔文 (K) 或摄氏度 (°C)。每个测量值都必须包含数值和单位。
m) means ÷1000, so 1000 mm = 1 m. Always convert quantities to base units before substituting them into formulas.
常见的前缀有助于表示非常大或非常小的量。千 (k) 表示 ×1000，因此 1 千米 = 1000 米。厘 (c) 表示 ÷100，因此 100 厘米 = 1 米。毫 (m) 表示 ÷1000，因此 1000 毫米 = 1 米。在将量代入公式之前，务必先把它们转换为基本单位。
2. Speed and the Motion Equation | 速度与运动方程
When an object moves at a constant speed, the relationship between distance, speed, and time is given by the formula. The average speed is the total distance travelled divided by the total time taken.
当物体匀速运动时，距离、速度和时间之间的关系由公式给出。平均速度等于总行进距离除以所用总时间。
speed = distance ÷ time
速度 = 距离 ÷ 时间
t, where v represents speed or velocity, s represents distance travelled, and t represents time taken. The unit of speed is metres per second (m/s).
用符号表示可以写作 v = s / t，其中 v 代表速度，s 代表行进距离，t 代表所用时间。速度的单位是米每秒 (m/s)。
distance and speed are known. To find distance use s = v × t. To find time use t = s / v.
你可以变换等式的写法，在已知速度和时间时求距离，或在已知距离和速度时求时间。求距离时用 s = v × t。求时间时用 t = s / v。
Example: A car travels 200 m in 10 s. Its speed is 200 m ÷ 10 s = 20 m/s.
示例：一辆汽车在 10 秒内行驶了 200 米。它的速度是 200 米 ÷ 10 秒 = 20 米/秒。
Example: A cyclist moves at 5 m/s for 30 s. Distance travelled is 5 m/s × 30 s = 150 m.
示例：一名骑自行车的人以 5 米/秒的速度骑行 30 秒。行进的距离是 5 米/秒 × 30 秒 = 150 米。
On a distance–time graph, a straight line represents constant speed. The gradient (steepness) of the line equals the speed. A steeper line means a higher speed.
在距离-时间图上，直线代表匀速运动。线的斜率（陡峭程度）等于速度。线越陡意味着速度越大。
3. Forces and Hooke's Law | 力与胡克定律
A force is a push or a pull. It is measured in newtons (N) using a force meter or spring balance. Forces can change the speed, direction, or shape of an object.
力是推力或拉力。它使用测力计或弹簧秤来测量，单位是牛顿 (N)。力可以改变物体的速度、方向或形状。
the following formula, where g is the gravitational field strength. On Earth, g ≈ 10 N/kg.
重量是作用在质量上的重力。它与质量通过以下公式关联，其中 g 是引力场强度。在地球上，g ≈ 10 牛/千克。
weight = mass × gravitational field strength
重量 = 质量 × 引力场强度
n kilograms and is the same everywhere. Weight is a force and can change depending on location, because g is different on other planets.
用符号表示，W = m × g。质量的单位是千克，无论在哪里都相同。重量是一种力，会因地点而改变，因为在其他行星上 g 值不同。
Hooke's Law describes the behaviour of a spring when it is stretched by a force. Up to its elastic limit, the extension of a spring is directly proportional to the force applied.
胡克定律描述了弹簧被力拉伸时的行为。在弹性限度内，弹簧的伸长量与所施加的力成正比。
F = k × x
Here F is the applied force in newtons, x is the extension in metres (how much longer the spring has become), and k is the spring constant measured in N/m. A stiffer spring has a larger spring constant.
此处 F 是施加的力，单位牛顿；x 是伸长量，单位米（弹簧变长了多少）；k 是弹簧常数，单位牛/米。弹簧越硬，弹簧常数越大。
4. Mass, Weight and Gravity | 质量、重量与重力
Mass is the amount of matter in an object. It is a scalar quantity, meaning it has size but no direction. Mass does not change whether you are on Earth, the Moon, or floating in space.
质量是物体所含物质的多少。它是一个标量，意味着有大小但没有方向。无论你是在地球上、月球上还是在太空中漂浮，质量都不会改变。
Weight is the gravitational force acting on an object. It is a vector quantity, meaning it has both size and direction (always pointing towards the centre of the planet).
重量是作用在物体上的引力。它是一个矢量，意味着既有大小又有方向（总是指向地心）。
On the Moon, g is about 1.6 N/kg, so your weight would be much smaller even though your mass is unchanged. On Jupiter, g is about 25 N/kg, making you feel very heavy.
公式 W = m × g 始终成立。在月球上，g 约为 1.6 牛/千克，所以即使质量不变，你的重量也会小得多。在木星上，g 约为 25 牛/千克，会让你感觉非常沉重。
| Location | g (N/kg) | Weight of 60 kg person (N) |
| Earth | 10 | 600 |
| Moon | 1.6 | 96 |
| Mars | 3.7 | 222 |
5. Friction and Terminal Speed | 摩擦与终极速度
Friction is a force that opposes motion between two surfaces in contact. It arises because surfaces are not perfectly smooth at the microscopic level. Air resistance (drag) is a type of friction that acts on objects moving through the air.
摩擦力是阻碍两个接触表面之间相对运动的力。它之所以产生，是因为表面在微观层面上并非完全光滑。空气阻力（拖曳力）是作用于在空气中运动的物体的一种摩擦力。
When an object falls through the air, two main forces act on it: weight pulling downwards and air resistance pushing upwards. At the start, the speed is low so air resistance is small, and the object accelerates downwards.
当物体在空气中下落时，两个主要的力作用在它身上：向下的重力和向上的空气阻力。开始时速度低，空气阻力小，物体向下加速。
As the speed increases, the air resistance force increases. Eventually, air resistance becomes equal to the weight. The resultant force is then zero, so the object stops accelerating and falls at a constant speed. This constant maximum speed is called terminal speed.
随着速度增加，空气阻力也增大。最终空气阻力与重量相等。此时合力为零，物体停止加速，以恒定速度下落。这个恒定的最大速度称为终极速度。
ardless of their mass. This acceleration due to gravity is the value g = 10 m/s² on Earth.
如果没有空气阻力（在真空中），所有物体无论质量大小都会以相同的速率加速。这个由重力引起的加速度在地球上的数值是 g = 10 米/秒²。
6. Density and Mass–Volume Relationship | 密度与质量-体积关系
Density describes how tightly packed the matter is inside a substance. It is calculated by dividing the mass of an object by its volume. The units of density are typically g/cm³ for solids and liquids, or kg/m³ for gases.
密度描述了物质内部物质的紧密程度。它通过物体的质量除以其体积来计算。密度的单位对于固体和液体通常是 克/厘米³，对于气体是 千克/米³。
density = mass ÷ volume
密度 = 质量 ÷ 体积
used for density). You can also rearrange to find mass (m = ρ × V) or volume (V = m / ρ).
用符号表示写作 ρ = m / V（希腊字母 rho, ρ，用于表示密度）。你也可以变换式子求质量 (m = ρ × V) 或体积 (V = m / ρ)。
An object will float on water if its density is less than 1 g/cm³. It will sink if its density is greater than 1 g/cm³.
如果物体的密度小于 1 克/厘米³，它会浮在水面上。如果密度大于 1 克/厘米³，它会下沉。
= length × width × height. Measure the mass with a balance, then use the density formula.
对于像立方体这样的规则固体，体积 = 长 × 宽 × 高。用天平测量质量，然后使用密度公式。
For an irregular solid, determine volume by water displacement in a measuring cylinder. The rise in water level equals the volume of the object.
对于不规则固体，通过在量筒中排水法来测定体积。水位上升的量等于物体的体积。
7. Energy Stores and the Conservation Law | 能量储存与守恒定律
Energy is the ability to do work and is measured in joules (J). Energy cannot be created or destroyed. This is the Principle of Conservation of Energy: energy can only be transferred from one store to another, or transferred between objects by heating, working, or radiating.
能量是做功的能力，单位是焦耳 (J)。能量不能被创造或毁灭。这就是能量守恒原理：能量只能从一个储存库转移到另一个储存库，或通过加热、做功或辐射在物体之间转移。
The main energy stores you need to know are: kinetic energy (movement), gravitational potential energy (position in a gravitational field), thermal energy (heat), chemical energy (stored in fuels and food), elastic potential energy (stretched or compressed objects), and electrostatic energy (attraction between electric charges).
你需要了解的主要能量储存库有：动能（运动的能量）、重力势能（在引力场中的位置）、热能（热量）、化学能（储存在燃料和食物中）、弹性势能（被拉伸或压缩的物体）和静电能量（电荷之间的吸引）。
The formula for kinetic energy depends on mass and speed. For gravitational potential energy, the formula relates mass, height, and gravitational field strength.
动能的公式取决于质量和速度。重力势能的公式则与质量、高度以及引力场强度有关。
Kinetic Energy = ½ × mass × speed²
动能 = ½ × 质量 × 速度²
Gravitational Potential Energy = mass × g × height
重力势能 = 质量 × g × 高度
In any process, the total energy at the start equals the total energy at the end. For a falling object, gravitational potential energy is transferred to kinetic energy. For a pendulum, energy continuously shifts between these two forms, but the total remains constant if we ignore friction.
在任何过程中，初始的总能量等于最终的总能量。对于下落的物体，重力势能转换为动能。对于钟摆，能量在这两种形式之间持续转换，但如果忽略摩擦，总能量保持不变。
8. Pressure, Force and Area | 压力、力与面积
Pressure is a measure of how concentrated a force is over a surface. A force applied over a small area creates a large pressure. The same force spread over a large area creates a small pressure.
压力是衡量力在一个表面上集中程度的量。作用在小面积上的力会产生大压力。同样的力分散在大面积上会产生小压力。
pressure = force ÷ area
压力 = 力 ÷ 面积
Pa), where 1 Pa = 1 N/m². The force is measured in newtons, and the area in square metres.
用符号表示，P = F / A。压力的单位是帕斯卡 (Pa)，1 帕 = 1 牛/米²。力的单位是牛顿，面积的单位是平方米。
Sharp knives cut easily because the force is concentrated on a very small area of the blade, producing very high pressure.
锋利的刀容易切割，因为力集中在刀刃非常小的面积上，产生极高的压力。
Snowshoes prevent a person from sinking into soft snow by increasing the area in contact with the ground, reducing the pressure underfoot.
雪鞋通过增加与地面接触的面积，降低脚下的压力，防止人陷入松软的雪中。
epth. The formula in a liquid is pressure = depth × density × g, written as P = h × ρ × g.
在液体中，压力随深度增加。液体中的公式是 压力 = 深度 × 密度 × g，写作 P = h × ρ × g。
9. Heat Transfer: Conduction, Convection, Radiation | 热传递：传导、对流、辐射
Thermal energy always moves from a region of higher temperature to a region of lower temperature. There are three main methods of heat transfer you must understand.
热能总是从温度较高的区域向温度较低的区域转移。你必须理解热传递的三种主要方式。
Conduction is the transfer of heat through a solid material without the material itself moving. It occurs because vibrating particles pass their energy to neighbouring particles. Metals are good conductors because they have free electrons that speed up heat transfer. Non-metals like wood and plastic are poor conductors (insulators).
传导是热量通过固体材料传递而材料本身不发生移动。它之所以发生，是因为振动的粒子将能量传递给相邻的粒子。金属是良导体，因为它们有自由电子可以加速热传递。像木材和塑料这样的非金属是不良导体（绝缘体）。
Convection occurs in liquids and gases. When a fluid is heated, it expands and becomes less dense. The warmer, less dense fluid rises, while cooler, denser fluid sinks to take its place. This creates a convection current that circulates heat through the entire fluid.
对流发生在液体和气体中。当流体被加热时，它会膨胀，密度变小。较热且密度较小的流体上升，而较冷且密度较大的流体下沉以取代其位置。这就形成了对流，使热量在整个流体中循环。
Radiation is the transfer of heat by infrared (thermal) electromagnetic waves. It does not require any particles or a medium, so heat can travel through the vacuum of space from the Sun to the Earth. Dark, matt surfaces are good absorbers and good emitters of radiation. Light, shiny surfaces are poor absorbers but good reflectors.
辐射是通过红外（热）电磁波传递热量。它不需要任何粒子或介质，因此热量可以通过真空从太阳传到地球。暗色粗糙的表面是辐射的良好吸收体和良好发射体。浅色光滑的表面吸收能力差，但反射能力好。
10. Wave Properties and the Wave Equation | 波的性质与波的方程
A wave is a disturbance that transfers energy from one place to another without transferring matter. Transverse waves have oscillations perpendicular to the direction of energy travel (e.g., light waves, water ripples). Longitudinal waves have oscillations parallel to the direction of energy travel (e.g., sound waves).
波是一种扰动，它将能量从一个地方传递到另一个地方而不传递物质。横波的振动方向垂直于能量传播方向（例如光波、水波）。纵波的振动方向平行于能量传播方向（例如声波）。
The wavelength (λ) is the distance between two successive identical points on a wave, such as crest to crest. The amplitude is the maximum displacement from the rest position, indicating the amount of energy a wave carries. The frequency (f) is the number of complete waves passing a point per second, measured in hertz (Hz).
波长 (λ) 是波上两个连续相同点之间的距离，例如波峰到波峰。振幅是离开平衡位置的最大位移，表明波携带能量的多少。频率 (f) 是每秒通过某点的完整波的数量，单位是赫兹 (Hz)。
taken for one complete wave to pass a point. It is the reciprocal of frequency: T = 1 / f.
波的周期 (T) 是一个完整波通过某点所需的时间。它是频率的倒数：T = 1 / f。
wave speed = frequency × wavelength
波速 = 频率 × 波长
measured in m/s, frequency f in Hz, and wavelength λ in metres. This equation applies to all types of wave, whether sound, light, or water waves.
用符号表示，v = f × λ。波速 v 的单位是 米/秒，频率 f 的单位是 Hz，波长 λ 的单位是米。这个方程适用于所有类型的波，无论是声波、光波还是水波。
11. Light, Reflection and Refraction | 光、反射与折射
cannot see around corners. The speed of light in a vacuum is approximately 3.0 × 10⁸ m/s.
光在均匀介质中沿直线传播。这解释了为什么阴影有清晰的边缘，以及为什么我们不能看到拐角后的东西。光在真空中的速度大约是 3.0 × 10⁸ 米/秒。
The Law of Reflection states that when a ray of light strikes a smooth surface, the angle of incidence (i) equals the angle of reflection (r). Both angles are measured relative to the normal, an imaginary line drawn perpendicular to the surface at the point of incidence.
反射定律指出，当一束光线照射到光滑表面时，入射角 (i) 等于反射角 (r)。这两个角都是相对于法线来测量的，法线是在入射点处画的一条垂直于表面的假想线。
angle of incidence = angle of reflection
入射角 = 反射角
The incident ray, the reflected ray, and the normal all lie in the same plane. A clear reflection image is produced by a plane (flat) mirror. The image is virtual (cannot be projected onto a screen), upright, and laterally inverted (left and right appear swapped).
入射线、反射线和法线都位于同一平面内。平面镜可以产生清晰的反射像。像是虚像（不能投射到屏上）、正立的，并且左右颠倒。
Refraction is the bending of light when it passes from one transparent medium to another of different density. When light enters a denser medium (e.g., from air into water), it slows down and bends towards the normal. When entering a less dense medium, it speeds up and bends away from the normal.
折射是光从一种透明介质进入另一种密度不同的介质时发生的弯曲。当光进入密度更大的介质时（例如从空气进入水），它会减慢速度并向法线弯曲。当进入密度较小的介质时，它会加速并偏离法线。
12. Electric Circuits and Ohm's Law | 电路与欧姆定律
An electric current is a flow of electric charge. Current (I) is measured in amperes (A), the potential difference or voltage (V) is measured in volts (V), and resistance (R) is measured in ohms (Ω).
电流是电荷的流动。电流 (I) 的单位是安培 (A)，电势差或电压 (V) 的单位是伏特 (V)，电阻 (R) 的单位是欧姆 (Ω)。
Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage across it, provided the temperature remains constant. This relationship gives us the most important formula in circuit analysis.
欧姆定律指出，在温度保持恒定的条件下，流过导体的电流与其两端的电压成正比。这个关系给出了电路分析中最重要的公式。
voltage = current × resistance
电压 = 电流 × 电阻
I). A component with a higher resistance allows less current to flow for the same voltage.
用符号表示，V = I × R。你也可以变换式子求电流 (I = V / R) 或电阻 (R = V / I)。在相同电压下，电阻越高的元件允许流过的电流越小。
In a series circuit, current is the same everywhere, but the total voltage is shared among the components. In a parallel circuit, voltage is the same across each branch, but the current splits and recombines at junctions.
在串联电路中，各处电流相同，但总电压分配给各个元件。在并联电路中，各支路两端电压相同，但电流在节点处分流并重新汇合。
Total resistance in series: Rₜₒₜₐₗ = R₁ + R₂ + R₃ …
串联电路的总电阻：Rₜₒₜₐₗ = R₁ + R₂ + R₃ …
For a parallel circuit, the total resistance is less than the smallest individual resistance. The effective resistance always decreases as more branches are added.
在并联电路中，总电阻小于最小的单个电阻。随着更多支路加入，等效电阻总是减小。
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