📚 Year 7 CAIE Engineering: Formulae & Theorems Quick Reference | Year 7 CAIE 工程：公式定理速查手册
This handbook gathers the most important equations and principles you will meet in Year 7 CAIE Engineering. Learning to use these relationships correctly will help you analyse forces, motion, energy, electricity and materials with confidence.
本手册汇集了 Year 7 CAIE 工程课程中最重要的公式和原理。学会正确运用这些关系将帮助你自信地分析力、运动、能量、电学和材料相关问题。
1. Force and Motion (Newton’s Second Law) | 力与运动（牛顿第二定律）
Newton’s Second Law tells us that the acceleration of an object depends on the net force acting on it and its mass. The equation is:
牛顿第二定律表明，物体的加速度取决于作用在其上的净力及其质量。方程为：
F = m × a
where F is force in newtons (N), m is mass in kilograms (kg) and a is acceleration in metres per second squared (m/s²).
其中 F 为力，单位牛顿 (N)；m 为质量，单位千克 (kg)；a 为加速度，单位米每二次方秒 (m/s²)。
Weight is the force of gravity acting on a mass. The formula is:
重量是作用在物体上的重力。公式为：
W = m × g
where W is weight in newtons (N) and g is the gravitational field strength. On Earth g ≈ 9.8 N/kg, often rounded to 10 N/kg.
其中 W 为重量，单位牛顿 (N)；g 为引力场强度。地球表面 g ≈ 9.8 N/kg，通常取 10 N/kg。
2. Work, Energy and Power | 功、能与功率
Work is done when a force makes an object move. The formula for work is:
当力使物体移动时就做了功。功的公式为：
W = F × d
where W is work done in joules (J), F is force in newtons (N) and d is distance moved in metres (m).
其中 W 为功，单位焦耳 (J)；F 为力 (N)；d 为移动距离 (m)。
Energy is the ability to do work. Gravitational potential energy (GPE) is stored because of an object’s height:
能量是做功的能力。重力势能 (GPE) 是由于物体所处高度而储存的能量：
GPE = m × g × h
where h is height in metres (m).
其中 h 为高度，单位米 (m)。
Kinetic energy (KE) is the energy of motion:
动能 (KE) 是运动的能量：
KE = ½ × m × v²
where v is speed in metres per second (m/s).
其中 v 为速度，单位米每秒 (m/s)。
Power is the rate at which work is done or energy is transferred:
功率是做功或能量转换的速率：
P = W / t
where P is power in watts (W) and t is time in seconds (s).
其中 P 为功率，单位瓦特 (W)；t 为时间，单位秒 (s)。
3. Pressure | 压强
Pressure measures how concentrated a force is over an area. The relationship is:
压强衡量力作用在面积上的集中程度。关系式为：
P = F / A
where P is pressure in pascals (Pa) or N/m², F is force in newtons (N) and A is area in square metres (m²).
其中 P 为压强，单位帕斯卡 (Pa) 或牛每平方米 (N/m²)；F 为力 (N)；A 为面积 (m²)。
A smaller area produces a larger pressure for the same force.
同样的力下，面积越小，压强越大。
4. Moments and Equilibrium | 力矩与平衡
A moment is the turning effect of a force. It is calculated by:
力矩是力的转动效应，计算公式为：
M = F × d
where M is the moment in newton-metres (Nm), F is the force in newtons (N) and d is the perpendicular distance from the pivot in metres (m).
其中 M 为力矩，单位牛顿·米 (Nm)；F 为力 (N)；d 为到支点的垂直距离 (m)。
For an object in equilibrium, the clockwise moments equal the anticlockwise moments:
物体处于平衡状态时，顺时针力矩之和等于逆时针力矩之和：
∑ clockwise moments = ∑ anticlockwise moments
∑ means ‘sum of’.
∑ 表示“总和”。
5. Density | 密度
Density relates mass to volume. The formula is:
密度将质量与体积联系起来。公式为：
ρ = m / V
where ρ (rho) is density in kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³), m is mass and V is volume.
其中 ρ (rho) 为密度，单位千克每立方米 (kg/m³) 或克每立方厘米 (g/cm³)；m 为质量，V 为体积。
6. Speed, Velocity and Acceleration | 速度、速率与加速度
Average speed is the total distance travelled divided by the total time taken:
平均速率等于总路程除以总时间：
v = d / t
where v is speed in m/s, d is distance (m) and t is time (s).
其中 v 为速率 (m/s)，d 为路程 (m)，t 为时间 (s)。
Acceleration is the rate of change of velocity. For uniform acceleration:
加速度是速度的变化率。对于匀加速运动：
a = (v – u) / t
where a is acceleration (m/s²), v is final speed (m/s), u is initial speed (m/s) and t is time (s).
其中 a 为加速度 (m/s²)，v 为末速度 (m/s)，u 为初速度 (m/s)，t 为时间 (s)。
7. Ohm’s Law and Circuits | 欧姆定律与电路
Ohm’s Law links voltage, current and resistance in a circuit:
欧姆定律将电路中的电压、电流和电阻联系起来：
V = I × R
where V is voltage in volts (V), I is current in amperes (A) and R is resistance in ohms (Ω).
其中 V 为电压，单位伏特 (V)；I 为电流，单位安培 (A)；R 为电阻，单位欧姆 (Ω)。
For resistors in series, the total resistance is the sum of individual resistances:
电阻串联时，总电阻等于各电阻之和：
R_total = R₁ + R₂ + R₃ + …
For resistors in parallel, the total resistance is found using:
电阻并联时，总电阻由下式求得：
1 / R_total = 1 / R₁ + 1 / R₂ + 1 / R₃ + …
Electrical power can be calculated by:
电功率可由以下公式计算：
P = I × V
where P is power in watts (W).
其中 P 为功率 (W)。
8. Mechanical Advantage (Levers, Pulleys, Gears) | 机械效益（杠杆、滑轮、齿轮）
Mechanical advantage (MA) tells us how many times a machine multiplies the effort force. For a lever:
机械效益 (MA) 表示机器将作用力放大了多少倍。对于杠杆：
MA = Load / Effort
or, using distances from the fulcrum:
或者利用距支点的距离：
MA = Effort arm length / Load arm length
For a pulley system, the ideal MA equals the number of rope segments that support the load.
对于滑轮组，理想机械效益等于支撑负载的绳索段数。
For gears, the gear ratio is:
对于齿轮，齿轮比为：
Gear ratio = Teeth on driven gear / Teeth on driver gear
A larger ratio gives more torque but less speed.
齿轮比越大，扭矩越大，但速度越慢。
9. Units and Conversions | 常用单位与换算
The table below summarises the quantity, unit and symbol for key measurements.
下表总结了关键物理量及其单位与符号。
| Quantity 物理量 | Unit 单位 | Symbol 符号 |
|---|---|---|
| Length | metre | m |
| Mass | kilogram |
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