📚 Year 7 Cambridge Engineering: Quick Guide to Formulas & Theorems | 剑桥七年级工程：公式定理速查手册
This handbook brings together all the essential formulas and theorems you will encounter in Year 7 Cambridge Engineering. From mechanics and energy to electricity and simple machines, each key relationship is explained clearly with units and worked examples.
本手册汇集了剑桥七年级工程课程中所有重要公式和定理。从力学、能量到电学与简单机械，每个关键关系都附有清晰的解释、单位和计算示例。
1. Speed, Distance and Time | 速度、距离与时间
Speed is a measure of how fast an object moves. The average speed can be calculated by dividing the total distance travelled by the time taken.
速度是物体运动快慢的量度。平均速度可以用通过的总距离除以所用时间来计算。
Speed = Distance ÷ Time
The standard units are metres per second (m/s) for science and kilometres per hour (km/h) for everyday travel.
标准单位在科学中用米每秒（m/s），日常交通中用千米每小时（km/h）。
If you need to find distance or time, the same formula can be rearranged: Distance = Speed × Time, and Time = Distance ÷ Speed.
如果需要求距离或时间，同一个公式可变形为：距离 = 速度 × 时间，时间 = 距离 ÷ 速度。
Example: A cyclist covers 300 metres in 20 seconds. Speed = 300 ÷ 20 = 15 m/s.
示例：一位自行车手在20秒内行驶300米。速度 = 300 ÷ 20 = 15 m/s。
2. Force, Mass and Acceleration | 力、质量与加速度
An unbalanced force causes an object to accelerate. The greater the mass, the more force is needed to achieve the same acceleration. This relationship is described by Newton’s Second Law.
不平衡的力使物体产生加速度。质量越大，获得同样加速度所需的力就越大。这一关系由牛顿第二定律描述。
Force = Mass × Acceleration
F = m × a
Force is measured in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). 1 N is the force needed to accelerate 1 kg at 1 m/s².
力的单位是牛顿（N），质量单位是千克（kg），加速度单位是米每二次方秒（m/s²）。1 N 是使 1 kg 物体产生 1 m/s² 加速度所需的力。
Example: A 10 kg cart accelerates at 2 m/s². The force needed is F = 10 × 2 = 20 N.
示例：一辆10 kg的小车以2 m/s²加速。所需的力为 F = 10 × 2 = 20 N。
3. Work, Energy and Power | 功、能量与功率
Work is done whenever a force moves an object in the direction of the force. The amount of work done equals the force multiplied by the distance moved.
只要力使物体沿力的方向移动，就做了功。做功的大小等于力乘以物体移动的距离。
Work = Force × Distance (in direction of force)
W = F × d
Work and energy are both measured in joules (J). One joule is equivalent to one newton metre.
功和能量都以焦耳（J）为单位。1焦耳等于1牛顿·米。
Energy is the ability to do work. Two key forms are kinetic energy (energy of motion) and gravitational potential energy (energy stored due to height).
能量是做功的本领。两种重要形式为动能（运动能量）和重力势能（因高度而储存的能量）。
Kinetic Energy = ½ × Mass × (Speed)²
Gravitational Potential Energy = Mass × gravitational field strength × Height (GPE = m × g × h)
On Earth, g ≈ 9.8 N/kg. Height is measured in metres (m).
地球上，g 约等于 9.8 N/kg。高度以米（m）为单位。
Power is the rate at which work is done or energy is transferred. A powerful machine does the same work in less time.
功率是做功或能量转换的速率。大功率的机器能在更短时间内完成相同的功。
Power = Work done ÷ Time taken or P = W / t
Power is measured in watts (W); 1 watt = 1 joule per second.
功率的单位是瓦特（W）；1瓦特 = 1焦耳每秒。
4. Levers and the Principle of Moments | 杠杆与力矩原理
A lever is a simple bar that turns around a fixed point called the fulcrum. It can multiply effort to lift a heavy load. The principle of moments states that for a balanced lever, the clockwise moment equals the anticlockwise moment.
杠杆是一根绕固定点（支点）转动的简单杆件，能放大动力以举起重负载。力矩原理表明，平衡的杠杆上，顺时针力矩等于逆时针力矩。
Effort × Effort arm = Load × Load arm
Feffort × deffort = Fload × dload
The effort arm is the distance from the effort to the fulcrum, and the load arm is the distance from the load to the fulcrum. If a 40 N effort is applied 2 m from the fulcrum, it can balance a 20 N load placed 4 m from the fulcrum.
动力臂是动力到支点的距离，阻力臂是负载到支点的距离。如果在距支点2 m处施加40 N的动力，就可以平衡距支点4 m处20 N的负载。
5. Pressure | 压力
Pressure describes how concentrated a force is over an area. A sharp knife cuts easily because it applies force over a very small area, creating high pressure.
压力描述了力在面积上的集中程度。锋利的刀容易切割，因为它将力施加在很小的面积上，产生了较大的压力。
Pressure = Force ÷ Area
P = F / A
The SI unit of pressure is the pascal (Pa), where 1 Pa = 1 N/m². A force of 100 N acting on an area of 2 m² produces a pressure of 50 Pa.
压力的国际单位是帕斯卡（Pa），1 Pa = 1 N/m²。100 N的力作用在2 m²的面积上，产生的压力为50 Pa。
6. Ohm’s Law | 欧姆定律
Ohm’s Law links voltage, current and resistance in a simple electrical circuit. As long as the temperature stays roughly constant, the current flowing through a resistor is directly proportional to the voltage across it.
欧姆定律连接了简单电路中的电压、电流和电阻。只要温度大致恒定，流过电阻的电流就与其两端的电压成正比。
Voltage = Current × Resistance
V = I × R
Voltage is measured in volts (V), current in amperes or amps (A), and resistance in ohms (Ω). If a 12 V battery is connected to a 4 Ω resistor, the current flowing is I = 12 ÷ 4 = 3 A.
电压以伏特（V）为单位，电流以安培（A）为单位，电阻以欧姆（Ω）为单位。如果12 V的电池连接到4 Ω的电阻上，流过电路的电流为 I = 12 ÷ 4 = 3 A。
7. Series and Parallel Circuits | 串联与并联电路
Components can be connected in series or in parallel. Each arrangement follows distinct rules for current, voltage and resistance.
元件可以串联或并联连接。两种连接方式在电流、电压和电阻上遵循不同的规则。
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Series circuit: Current is the same at all points (Itotal = I1 = I2). The total voltage is the sum of individual voltages (Vtotal = V1 + V2). Total resistance adds up (Rtotal = R1 + R2).
串联电路：各处电流相同（I总 = I1 = I2）。总电压等于各元件电压之和（V总 = V1 + V2）。总电阻为各电阻之和（R总 = R1 + R2）。
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Parallel circuit: Voltage is the same across each branch (Vtotal = V1 = V2). The total current splits between branches (Itotal = I1 + I2). For two resistors in parallel, the total resistance can be found using: Rtotal = (R1 × R2) ÷ (R1 + R2).
并联电路：各支路两端电压相同（V总 = V1 = V2）。总电流为各支路电流之和（I总 = I1 + I2）。对于两个电阻并联，总电阻可用下式计算：R总 = (R1 × R2) ÷ (R1 + R2)。
The table below summarises these key differences.
下表总结了这些主要区别。
| Quantity | Series Circuit | Parallel Circuit |
|---|---|---|
| Current | Same everywhere 各处相等 |
Splits between branches 各支路分流 |
| Voltage | Divided across components 各元件分压 |
Same across each branch 各支路电压相同 |
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