📚 Year 7 Cambridge Engineering: Formula & Theorem Quick Reference Handbook | 剑桥7年级工程：公式定理速查手册
This handbook provides a handy summary of the essential formulas and theorems you will encounter in Year 7 Cambridge Engineering. Understanding and memorising these relationships will help you design structures, analyse mechanisms, and solve real-world problems efficiently. Keep this guide close during revision and practical work.
本手册总结了你在剑桥7年级工程课程中会用到的重要公式和定理。理解并熟记这些关系将帮助你设计结构、分析机构并高效解决实际问题。复习和动手实践时可随时参考本手册。
1. Speed, Distance and Time | 速度、距离与时间
Speed describes how fast an object moves. It is the distance travelled divided by the time taken. The formula is:
速度描述物体运动的快慢，等于通过的距离除以所用的时间。公式如下：
v = d / t
Where v is speed (m/s), d is distance (m), and t is time (s). You can rearrange this to find distance (d = v × t) or time (t = d / v).
其中 v 是速度（米/秒），d 是距离（米），t 是时间（秒）。你可以通过变形计算距离 (d = v × t) 或时间 (t = d / v)。
2. Force, Mass and Weight | 力、质量与重量
A force is a push or a pull that can change an object’s motion. Weight is a specific force caused by gravity acting on a mass. The relationship is given by:
力是能改变物体运动的推或拉。重量是重力作用于质量而产生的特定力。二者关系为：
W = m × g
Here W stands for weight (N), m is mass (kg), and g is gravitational field strength, which on Earth is approximately 10 N/kg. Remember that mass does not change with location, but weight does.
式中 W 表示重量（牛顿），m 是质量（千克），g 是引力场强度，在地球上约为 10 N/kg。注意质量不随位置改变，但重量会变。
3. Pressure | 压强
Pressure measures how concentrated a force is over an area. A sharp knife cuts easily because it applies high pressure. The formula is:
压强衡量力在面积上的集中程度。锋利的刀容易切割，因为它产生高压强。公式为：
P = F / A
P is pressure (N/m² or Pascals, Pa), F is force (N), and A is area (m²). Increasing force or decreasing area raises pressure.
P 是压强（牛/米² 或帕斯卡 Pa），F 是力（牛顿），A 是面积（米²）。增大作用力或减小受力面积都会使压强增大。
4. Moments | 力矩
A moment is the turning effect of a force around a pivot. It depends on the size of the force and its distance from the pivot. The equation is:
力矩是力使物体绕支点转动的效果，取决于力的大小及其到支点的距离。公式为：
M = F × d
M represents moment (Newton-metres, Nm), F is force (N), and d is the perpendicular distance from the pivot (m). For an object to balance, the total clockwise moments must equal the total anticlockwise moments.
M 表示力矩（牛顿·米，Nm），F 是力（牛顿），d 是支点到力作用线的垂直距离（米）。要使物体平衡，顺时针力矩之和必须等于逆时针力矩之和。
5. Levers and Mechanical Advantage | 杠杆与机械效益
Levers are simple machines that multiply effort. Mechanical advantage (MA) tells us how many times a lever multiplies the input force. The formula is:
杠杆是能放大作用力的简单机械。机械效益 (MA) 表示杠杆将输入力放大了多少倍。公式为：
MA = Load / Effort
Load is the force you need to overcome (N), and Effort is the force you apply (N). A mechanical advantage greater than 1 means the lever makes the job easier.
Load 是需要克服的力（牛顿），Effort 是施加的力（牛顿）。机械效益大于 1 意味着杠杆省力。
For a first-class lever in equilibrium, the principle of moments also gives: Effort × Effort distance = Load × Load distance.
对于平衡状态下的一类杠杆，力矩原理还给出：作用力 × 作用力臂 = 负载 × 负载臂。
6. Gear Ratios | 齿轮比
Gears transmit rotation and can change speed and torque. The gear ratio compares the number of teeth on the driven gear to the number on the driver gear:
齿轮传递转动并能改变转速和扭矩。齿轮比是指从动齿轮齿数与主动齿轮齿数之比：
Gear Ratio = Teeth on driven gear / Teeth on driver gear
A ratio greater than 1 reduces speed but increases torque (force). A ratio less than 1 increases speed but reduces torque. Output speed can be found using: Output speed = Input speed / Gear ratio.
比值大于 1 会降低转速但增大扭矩（力）。比值小于 1 则提高转速但减小扭矩。输出转速可用公式：输出转速 = 输入转速 ÷ 齿轮比。
7. Work and Energy | 功与能
Work is done when a force moves an object. Energy is the ability to do work, and both are measured in joules (J). The formula for work done is:
力使物体移动时就做了功。能量是做功的能力，两者单位均为焦耳 (J)。计算做功的公式是：
W = F × d
W is work done (J), F is force (N), and d is distance moved in the direction of the force (m). In mechanical systems, energy can be transferred but is always conserved.
W 是做功（焦耳），F 是力（牛顿），d 是沿力方向移动的距离（米）。在机械系统中，能量可以转移，但总是守恒的。
8. Power | 功率
Power tells us how quickly work is done or energy is transferred. The formula is:
功率表示做功或传递能量的快慢。公式为：
P = W / t
P is power (watts, W), W is work done (J), and t is time (s). One watt equals one joule per second. In electrical engineering, power is also calculated using voltage and current (see section 9).
P 是功率（瓦特，W），W 是功（焦耳），t 是时间（秒）。1 瓦等于每秒 1 焦耳。在电气工程中，功率也可通过电压和电流计算（见第9节）。
9. Ohm’s Law and Electrical Power | 欧姆定律与电功率
Ohm’s Law connects voltage, current and resistance in a circuit:
欧姆定律联系电路中的电压、电流和电阻：
V = I × R
V is voltage (volts, V), I is current (amperes, A), and R is resistance (ohms, Ω). This law is essential for designing and analysing electrical components.
V 是电压（伏特，V），I 是电流（安培，A），R 是电阻（欧姆，Ω）。这一定律对于设计和分析电气元件至关重要。
To find electrical power, combine Ohm’s Law with the power equation:
要计算电功率，可结合欧姆定律和功率方程：
P = I × V
P is power (W), I is current (A), and V is voltage (V). This formula helps you select the correct fuse and calculate energy consumption.
P 是功率（瓦特），I 是电流（安培），V 是电压（伏特）。该公式可帮你选择正确的保险丝并计算能耗。
10. Density | 密度
Density describes how much mass is packed into a given volume. It helps engineers choose materials for different applications. The formula is:
密度表示单位体积内所含质量的多少，帮助工程师根据不同用途选择材料。公式为：
ρ = m / V
ρ (pronounced ‘rho’) is density (g/cm³ or kg/m³), m is mass (g or kg), and V is volume (cm³ or m³). Materials with lower density, like aluminium, are often used where weight saving is important.
ρ（读作“柔”）是密度（克/厘米³ 或 千克/米³），m 是质量（克 或 千克），V 是体积（厘米³ 或 米³）。像铝这样密度较小的材料常用于需要减轻重量的场合。
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