📚 Year 8 OCR Engineering Formula & Theorem Quick Reference Handbook | Year 8 OCR 工程：公式定理速查手册
Welcome to your Year 8 OCR Engineering quick reference. This handbook brings together the essential formulas, key theorems and core principles you need for the course. Use it to revise, check your work and build confidence before assessments.
欢迎使用这本 Year 8 OCR 工程速查手册。本手册汇集了课程所需的基本公式、重要定理和核心原理。你可以用它来复习、检查作业，并在评估前建立信心。
1. Force, Mass and Acceleration | 力、质量与加速度
The resultant force on an object is equal to its mass multiplied by its acceleration. This is Newton's Second Law.
作用在物体上的合力等于其质量乘以加速度。这是牛顿第二定律。
F = m × a
Force (F) is measured in newtons (N), mass (m) in kilograms (kg) and acceleration (a) in metres per second squared (m/s²).
力（F）的单位是牛顿（N），质量（m）的单位是千克（kg），加速度（a）的单位是米每平方秒（m/s²）。
2. Weight and Gravitational Field Strength | 重力与引力场强度
Weight is the force due to gravity acting on a mass. On Earth, gravitational field strength (g) is about 9.8 N/kg, but 10 N/kg is often used for estimation.
重量是作用在质量上的重力。地球上的引力场强度（g）约为 9.8 N/kg，但估算时经常使用 10 N/kg。
W = m × g
Weight (W) is in newtons, mass (m) in kilograms. Never confuse mass and weight – mass is the amount of matter, weight is a force.
重量（W）的单位是牛顿，质量（m）的单位是千克。切勿混淆质量与重量——质量是物质的多少，重量是一种力。
3. Moments and Turning Effect | 力矩与转动效应
A moment is the turning effect of a force about a pivot. It depends on the size of the force and the perpendicular distance from the pivot.
力矩是力绕支点产生的转动效应。它取决于力的大小和到支点的垂直距离。
M = F × d
Moment (M) is in newton-metres (Nm), force (F) in newtons and perpendicular distance (d) in metres. For a system in equilibrium, total clockwise moments equal total anticlockwise moments.
力矩（M）的单位是牛顿米（Nm），力（F）的单位是牛顿，垂直距离（d）的单位是米。对于处于平衡状态的系统，总顺时针力矩等于总逆时针力矩。
4. Pressure in Solids and Fluids | 固体与流体的压强
Pressure is the force acting perpendicularly per unit area. A smaller contact area creates greater pressure for the same force.
压强是垂直作用在单位面积上的力。对于相同的力，接触面积越小，压强越大。
P = F ÷ A
Pressure (P) is in pascals (Pa) or N/m², force (F) in newtons, area (A) in square metres. In fluids, pressure increases with depth and acts equally in all directions.
压强（P）的单位是帕斯卡（Pa）或 N/m²，力（F）的单位是牛顿，面积（A）的单位是平方米。在流体中，压强随深度增加，且在所有方向上同等作用。
5. Work Done and Energy Transfer | 做功与能量转化
Work is done when a force moves an object through a distance in the direction of the force. Work done equals the energy transferred.
当力使物体沿力的方向移动一段距离时，就做了功。所做的功等于传递的能量。
W = F × d
Work (W) is in joules (J), force (F) in newtons, distance (d) in metres. The distance must be measured along the line of action of the force.
功（W）的单位是焦耳（J），力（F）的单位是牛顿，距离（d）的单位是米。距离必须沿着力的作用线测量。
6. Power and Rate of Energy Transfer | 功率与能量转化率
Power is the rate at which work is done or energy transferred. A more powerful machine does the same work in less time.
功率是做功或能量转移的速率。更强大的机器可以在更短的时间内完成相同的功。
P = W ÷ t and P = E ÷ t
Power (P) is in watts (W), work or energy (W/E) in joules, time (t) in seconds. One watt is one joule per second.
功率（P）的单位是瓦特（W），功或能量（W/E）的单位是焦耳，时间（t）的单位是秒。一瓦特等于一焦耳每秒。
7. Efficiency of Systems | 系统效率
No machine is 100% efficient; some energy is always dissipated, often as heat due to friction. Efficiency compares useful output to total input.
没有机器是 100% 高效的；总有一些能量被耗散，通常是由于摩擦转化为热量。效率比较有用输出和总输入。
Efficiency = (Useful output energy ÷ Total input energy) × 100%
It can also be expressed in terms of power. Efficiency has no unit; it is a ratio, often given as a percentage.
效率也可以用功率来表示。效率没有单位；它是一个比值，通常以百分比给出。
8. Mechanical Advantage and Velocity Ratio | 机械利益与速度比
Simple machines help to multiply force or change its direction. Mechanical advantage tells you how much the machine amplifies the effort force.
简单机械有助于放大力量或改变力的方向。机械利益告诉你机器将施加的力放大了多少。
MA = Load ÷ Effort
moved by effort to distance moved by load. For an ideal machine with no friction, MA = VR.
速度比是动力移动的距离与负载移动的距离之比。对于没有摩擦的理想机器，MA = VR。
VR = Distance moved by effort ÷ Distance moved by load
9. Ohm’s Law and Basic Circuits | 欧姆定律与基础电路
In an electrical circuit, the current through a resistor is directly proportional to the voltage across it, provided temperature remains constant.
在电路中，只要温度保持恒定，通过电阻的电流与其两端的电压成正比。
V = I × R
Voltage (V) in volts, current (I) in amperes, resistance (R) in ohms (Ω). A series circuit has one path; a parallel circuit has multiple branches.
电压（V）的单位是伏特，电流（I）的单位是安培，电阻（R）的单位是欧姆（Ω）。串联电路只有一条路径；并联电路有多个分支。
10. Electrical Power and Energy | 电功率与电能
Electrical power is the product of current and voltage. It describes how quickly an appliance transfers electrical energy into other forms.
电功率是电流和电压的乘积。它描述了用电器将电能转化为其他形式能量的快慢。
P = I × V
Energy transferred by an appliance can be calculated from its power rating and the time it is switched on.
用电器传递的能量可以通过其额定功率和开启时间来计算。
E = P × t
11. Density and Material Properties | 密度与材料性质
Density links the mass of a material to the volume it occupies. Engineering materials are chosen for their density, strength and stiffness.
密度将材料的质量与其占据的体积联系起来。工程材料的选择基于其密度、强度和刚度。
ρ = m ÷ V
Density (ρ) in kg/m³, mass (m) in kilograms, volume (V) in cubic metres. The same formula applies when using g and cm³.
密度（ρ）的单位是 kg/m³，质量（m）的单位是千克，体积（V）的单位是立方米。当使用克和立方厘米时，公式同样适用。
12. Hooke’s Law and Elastic Behaviour | 胡克定律与弹性行为
For a spring or elastic material, extension is directly proportional to the applied force, up to the limit of proportionality.
对于弹簧或弹性材料，在比例极限以内，伸长量与施加的力成正比。
F = k × e
Force (F) in newtons, spring constant (k) in N/m, extension (e) in metres. The stiffer the spring, the greater the value of k.
力（F）的单位是牛顿，弹簧常数（k）的单位是 N/m，伸长量（e）的单位是米。弹簧越硬，k 值越大。
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