📚 Year 7 CAIE Physics: Formula and Theorem Quick Reference Handbook | Year 7 CAIE 物理：公式定理速查手册
This quick reference handbook covers all the key formulas and theorems you need for Year 7 CAIE Physics. Use it to revise essential principles, from speed and density to electricity and waves. Each section pairs a concise English explanation with a matching Chinese version to help bilingual learners.
本速查手册涵盖 Year 7 CAIE 物理所需的所有关键公式和定理。使用它复习从速度、密度到电学和波的各种基本原理。每个部分都将简洁的英文解释与中文配对，以帮助双语学习者。
1. Physical Quantities, Units and Measurement | 物理量、单位与测量
All physical quantities consist of a numerical value and a unit. The International System of Units (SI) defines baseline units for length, mass, time and temperature.
所有物理量都由数值和单位组成。国际单位制 (SI) 定义了长度、质量、时间和温度的基本单位。
| Quantity | Symbol | SI Unit | Unit Symbol | Common measuring tool |
|---|---|---|---|---|
| Length | l, d, h | metre | m | Ruler, measuring tape |
| Mass | m | kilogram | kg | Electronic balance, beam balance |
| Time | t | second | s | Stopwatch, digital timer |
| Temperature | T, θ | kelvin / degree Celsius | K, ℃ | Thermometer |
| Volume (regular solid) | V | cubic metre | m³ | Ruler (length × width × height) |
| Volume (liquid) | V | litre or cubic centimetre | L, cm³ | Measuring cylinder, pipette |
Volume formulas for regular shapes:
规则形状的体积公式：
Volume of a cuboid V = l × w × h
Use the same length unit for all dimensions. For a cylinder, V = π r² h (π ≈ 3.14).
所有尺寸使用相同的长度单位。对于圆柱体，V = π r² h (π ≈ 3.14)。
When measuring, always avoid parallax error by reading the scale at eye level. Record readings using the correct precision.
测量时务必通过视线水平读数以避免视差。以正确的精度记录读数。
2. Motion and Speed | 运动与速度
Speed is the distance travelled per unit time. It is a scalar quantity; velocity includes direction and is a vector.
速度是单位时间内通过的距离。速率是标量；速度包含方向，是矢量。
Average speed v = s / t
Where s = distance travelled (m), t = time taken (s). The SI unit of speed is metre per second (m/s).
其中 s = 行驶距离（米），t = 所用时间（秒）。速度的国际单位是米每秒（m/s）。
On a distance–time graph, a straight sloping line shows constant speed. The gradient (slope) equals the speed. A horizontal line means the object is stationary.
在距离-时间图中，倾斜直线表示匀速运动。斜率即为速度。水平线表示物体静止。
Average speed is total distance divided by total time. Instantaneous speed is the speed at a particular instant and can be read from a speedometer.
平均速度 = 总距离 ÷ 总时间。瞬时速度是某一瞬间的速度，可从速度计上读取。
3. Mass, Weight and Gravity | 质量、重量与重力
Mass is the amount of matter in an object; it does not change with location. Weight is the gravitational force acting on a mass and varies with the strength of gravity.
质量是物体所含物质的多少，不随位置改变。重量是作用在质量上的重力，随重力强度变化。
Weight W = m × g
m = mass (kg), g = gravitational field strength (N/kg). On Earth g ≈ 9.8 N/kg; often rounded to 10 N/kg for calculations. Weight is a force measured in newtons (N).
m = 质量（千克），g = 重力场强度（牛/千克）。地球上 g ≈ 9.8 N/kg，计算时常取 10 N/kg。重量是一种力，单位牛顿 (N)。
The mass of an object is measured with a balance; weight is measured with a spring balance or force meter. On the Moon, g is about 1.6 N/kg, so your weight would be much smaller while your mass stays constant.
质量用天平测量；重量用弹簧秤或测力计测量。月球上 g 约 1.6 N/kg，因此你的重量会小得多，但质量不变。
4. Density | 密度
Density describes how tightly packed the matter is within a substance. It links mass and volume.
密度描述物质中物质的紧密程度。它将质量与体积联系起来。
Density ρ = m / V
ρ (rho) is density, m is mass, V is volume. Common units: kg/m³ or g/cm³ (1 g/cm³ = 1000 kg/m³).
ρ (rho) 为密度，m 为质量，V 为体积。常用单位：kg/m³ 或 g/cm³ (1 g/cm³ = 1000 kg/m³)。
An object floats if its density is less than the density of the fluid it is placed in; it sinks if its density is greater. The density of water is about 1.0 g/cm³.
物体密度小于所处流体密度时会漂浮；大于时会下沉。水的密度约为 1.0 g/cm³。
To find the density of an irregular solid: measure its mass on a balance, then find its volume by displacement of water in a measuring cylinder.
测量不规则固体密度的方法：用天平测质量，再用排水法在量筒中测体积。
5. Pressure | 压强
Pressure is the force acting perpendicularly per unit area. A small force can produce a very large pressure if it is concentrated on a tiny area.
压强是垂直作用于单位面积上的力。如果力集中在微小面积上，很小的力也能产生很大压强。
Pressure p = F / A
p = pressure (pascal, Pa), F = force (N), A = area (m²). 1 Pa = 1 N/m².
p = 压强（帕斯卡 Pa），F = 力（牛），A = 面积（平方米）。1 Pa = 1 N/m²。
To increase pressure: increase the force, or reduce the area (e.g. sharp knife, needle). To decrease pressure: decrease the force, or increase the area (e.g. snow shoes, wide tyres).
增大压强：增大压力或减小面积（如锋利的刀、针）。减小压强：减小压力或增大面积（如雪鞋、宽轮胎）。
Liquid pressure increases with depth and density, and acts equally in all directions at a given depth.
液体压强随深度和密度增大而增大，在同一深度各个方向压强相等。
6. Energy, Work and Power | 能量、功与功率
Energy is the ability to do work. It can be stored (potential) or associated with motion (kinetic). The law of conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another.
能量是做功的能力。能量可以储存（势能）或与运动相关（动能）。能量守恒定律指出，能量既不能创造也不能消灭，只能转移或从一种形式转化为另一种形式。
Kinetic energy Eₖ = 1/2 m v²
Eₖ = kinetic energy (J), m = mass (kg), v = speed (m/s).
Eₖ = 动能（焦耳），m = 质量（千克），v = 速度（米/秒）。
Change in gravitational potential energy Eₚ = m g h
Eₚ = gravitational potential energy (J), m = mass (kg), g = gravitational field strength, h = height change (m).
Eₚ = 重力势能（焦耳），m = 质量（千克），g = 重力场强度，h = 高度变化（米）。
Work is done when a force moves an object in the direction of the force.
当力使物体沿力的方向移动时，就做了功。
Work done W = F × d
W = work (J), F = force (N), d = distance moved in direction of force (m).
W = 功（焦耳），F = 力（牛），d = 沿力方向移动的距离（米）。
Power is the rate of doing work or transferring energy.
功率是做功或能量转移的速率。
Power P = W / t or P = E / t
P = power (watt, W), W = work done (J), E = energy transferred (J), t = time (s). 1 W = 1 J/s.
P = 功率（瓦特 W），W = 做功（焦），E = 转移的能量（焦），t = 时间（秒）。1 W = 1 J/s。
7. Heat Transfer | 热传递
Heat can travel in three ways: conduction, convection and radiation. No net heat transfer occurs when two objects reach the same temperature (thermal equilibrium).
热传递有三种方式：传导、对流和辐射。当两个物体达到相同温度时，净传热停止（热平衡）。
Conduction: Transfer of heat through a solid without the material moving. Metals are good conductors; non-metals and gases are insulators.
传导：热量通过固体传递而物质本身不移动。金属是良导体；非金属和气体是绝缘体。
Convection: Transfer of heat in fluids (liquids and gases) by the movement of the fluid itself. Hot fluid rises, cool fluid sinks, forming convection currents.
对流：热量通过流体（液体和气体）自身的运动传递。热流体上升，冷流体下沉，形成对流循环。
Radiation: Transfer of heat by infrared electromagnetic waves. Can travel through vacuum. Dull, black surfaces are good absorbers and emitters; shiny, light surfaces are poor absorbers and good reflectors.
辐射：热量通过红外电磁波传递，可在真空中传播。暗黑色表面是良吸收体和良辐射体；光亮浅色表面吸收差、反射好。
Thermal expansion: Most substances expand when heated and contract when cooled. This principle is used in liquid-in-glass thermometers.
热胀冷缩：大多数物质受热膨胀，冷却收缩。液体温度计应用了这一原理。
8. Waves: Light and Sound | 波：光与声
Both light and sound travel as waves. Light is a transverse electromagnetic wave that can travel through a vacuum; sound is a longitudinal mechanical wave that requires a medium.
光与声都以波的形式传播。光是横波，属于电磁波，可在真空中传播；声是纵波，属于机械波，需要介质。
Wave speed v = f × λ
v = wave speed (m/s), f = frequency (hertz, Hz), λ = wavelength (m).
v = 波速（米/秒），f = 频率（赫兹 Hz），λ = 波长（米）。
- Speed of light in vacuum c ≈ 3.0 × 10⁸ m/s — 真空光速 c ≈ 3.0 × 10⁸ m/s
- Speed of sound in air at room temperature ≈ 340 m/s — 室温空气中声速 ≈ 340 m/s
Law of reflection: The angle of incidence (i) equals the angle of reflection (r), both measured from the normal. The incident ray, reflected ray and normal all lie in the same plane.
反射定律：入射角 (i) 等于反射角 (r)，都从法线量起。入射线、反射线和法线位于同一平面内。
Refraction: When light passes from one medium to another, its speed changes, causing it to bend. Light bends towards the normal when entering a denser medium and away from the normal when entering a less dense medium.
折射：光从一种介质斜射入另一种介质时速度改变，导致偏折。进入光密介质时偏向法线；进入光疏介质时偏离法线。
Sound travels fastest in solids, slower in liquids and slowest in gases. Pitch depends on frequency; loudness depends on amplitude.
声音在固体中传播最快，液体中次之，气体中最慢。音高取决于频率；响度取决于振幅。
9. Electricity | 电学
Current (I) is the rate of flow of charge; it is measured in amperes (A) using an ammeter connected in series. Voltage (V) is the energy transferred per unit charge; it is measured in volts (V) using a voltmeter connected in parallel. Resistance (R) opposes current flow and is measured in ohms (Ω).
电流 (I) 是电荷流动的速率，单位安培 (A)，用串联的电流表测量。电压 (V) 是每单位电荷转移的能量，单位伏特 (V)，用并联的电压表测量。电阻 (R) 阻碍电流流动，单位欧姆 (Ω)。
Ohm’s Law: V = I × R
For a conductor at constant temperature, current is directly proportional to voltage.
对于温度不变的导体，电流与电压成正比。
Series circuits:
串联电路：
- Current is the same everywhere: I_total = I₁ = I₂ — 各处电流相等：I_total = I₁ = I
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