📚 Year 8 AQA Engineering: Formulas & Theorems Quick Reference Handbook | Year 8 AQA 工程：公式定理速查手册
This quick reference handbook brings together the essential formulas, rules and theorems you will meet in the Year 8 AQA Engineering course. Use it alongside practical work to build confidence in calculations and problem‑solving. The topics range from forces and simple machines to electricity and material behaviour.
本速查手册汇总了 Year 8 AQA 工程课程中必备的公式、法则和定理。配合实践环节使用，可帮助你提高计算与问题解决的信心。内容涵盖力与简单机械、电学以及材料行为等多个领域。
1. Forces and Moments | 力与力矩
The moment of a force (also called torque) measures its turning effect about a pivot. It is calculated by multiplying the size of the force by the perpendicular distance from the pivot to the line of action of the force.
力矩（也称扭矩）衡量力绕支点产生的转动效应。它等于力的大小乘以从支点到力作用线的垂直距离。
M = F × d
Moment (M) is measured in newton metres (N m), force (F) in newtons (N) and perpendicular distance (d) in metres (m).
力矩（M）的单位是牛·米（N m），力（F）的单位是牛（N），垂直距离（d）的单位是米（m）。
When a lever, beam or object is balanced (in equilibrium), the sum of the clockwise moments equals the sum of the anticlockwise moments about the same pivot.
当杠杆、梁或物体平衡（处于平衡状态）时，围绕同一支点，顺时针力矩之总和等于逆时针力矩之总和。
∑Mcw = ∑Macw
2. Simple Machines: Levers and Linkages | 简单机械：杠杆与连杆
ee classes of lever, but they all obey the same principle: effort × effort arm = load × load arm.
杠杆是能绕固定支点（铰点）转动的刚性杆，它可用来放大作用力或改变作用方向。杠杆分为三类，但它们都遵循同一原理：动力 × 动力臂 = 阻力 × 阻力臂。
E × dE = L × dL
Here E is the effort force, dE is the distance from the fulcrum to the effort, L is the load force, and dL is the distance from the fulcrum to the load. The lever gives a mechanical advantage when dE > dL.
式中 E 为动力，dE 为支点到动力点的距离，L 为负载阻力，dL 为支点到负载点的距离。当 dE > dL 时，杠杆能提供机械效益。
Linkages are connected levers that transmit force and motion. Their output motion can change direction, amplitude or type (e.g. rotary to linear).
连杆是由杠杆连接而成的机构，用于传递力与运动。其输出运动可以改变方向、幅度或类型（例如回转运动转换为直线运动）。
3. Mechanical Advantage and Velocity Ratio | 机械效益与速度比
Mechanical advantage (MA) tells us how many times a machine multiplies the input force. It is the ratio of the load to the effort.
机械效益（MA）表示机器将输入力放大的倍数，它等于负载与动力的比值。
MA = L / E
Velocity ratio (VR) compares the distance moved by the effort to the distance moved by the load in the same time. It depends only on the design of the machine.
速度比（VR）比较同一时间内动力移动的距离与负载移动的距离，它只取决于机器的设计。
VR = dE / dL
e with no friction, MA = VR. In real machines, friction makes MA slightly smaller than VR.
在无摩擦的理想机器中，MA = VR。在实际机器中，摩擦会使 MA 略小于 VR。
4. Efficiency of Systems | 系统的效率
Efficiency describes how well a machine converts input energy into useful output work. It is often expressed as a percentage.
效率描述机器将输入能量转化为有用输出功的程度，通常用百分数表示。
η = (useful work output / total energy input) × 100%
The Greek letter η (eta) stands for efficiency. Both work output and energy input are measured in joules (J). An ideal system would have an efficiency of 100%, but practical systems are always lower because of friction, sound and heat losses.
希腊字母 η（伊塔）代表效率。输出功和输入能量均以焦耳（J）为单位。理想系统的效率为 100%，但实际系统因摩擦、声音和热损耗，效率总是低于该值。
can also be calculated using mechanical advantage and velocity ratio: η = (MA / VR) × 100%. This form is handy when testing a mechanism.
效率也可用机械效益和速度比计算：η = (MA / VR) × 100%。在测试机构时，这一形式非常实用。
5. Gears and Gear Ratios | 齿轮与齿轮比
Gear systems transmit rotary motion and torque between shafts. The gear ratio relates the number of teeth on the driven gear to the number of teeth on the driver gear.
齿轮系统在轴之间传递回转运动和扭矩。齿轮比是从动轮齿数与主动轮齿数之比。
Gear ratio = Tdriven / Tdriver
Because the teeth mesh, the rotational speeds (N) are inversely proportional to the number of teeth. If the driven gear has more teeth, it turns more slowly but with greater torque.
由于轮齿啮合，转速（N）与齿数成反比。若从动轮齿数更多，其转速较慢，但扭矩更大。
Ndriver / Ndriven = Tdriven / Tdriver
Compound gear trains can achieve large overall ratios by multiplying ratios of successive pairs.
复式轮系可通过逐对齿轮比的乘积获得很大的总传动比。
6. Pulleys and Belt Drives | 滑轮与皮带传动
A simple pulley changes the direction of a force; its MA is 1 and VR is 1. Adding more rope sections in a block and tackle system increases the mechanical advantage.
单个定滑轮只改变力的方向，其 MA = 1，VR = 1。在滑轮组中增加绳索段数可提高机械效益。
VR = number of rope sections supporting the load
For belt and pulley drives, the speed ratio is determined by the diameters (D) of the pulleys. A smaller pulley driving a larger one reduces speed but increases torque.
对于皮带和带轮传动，转速比由带轮直径（D）决定。小轮驱动大轮会降速增扭。
Ndriver / Ndriven = Ddriven / Ddriver
The belt drive can slip under overload, which can protect the machine but reduces accuracy.
皮带传动在过载时可打滑，这能保护机器，但会降低传动精度。
7. Basic Electricity: Ohm’s Law and Power | 基础电学：欧姆定律与功率
Ohm’s Law links voltage (V), current (I) and resistance (R) in a circuit. It is one of the most important relationships in electrical engineering.
欧姆定律将电路中的电压（V）、电流（I）和电阻（R）联系在一起，是电气工程中最重要的关系式之一。
V = I × R
Voltage is measured in volts (V), current in amperes (A) and resistance in ohms (Ω).
电压的单位是伏特（V），电流的单位是安培（A），电阻的单位是欧姆（Ω）。
Electrical power is the rate at which electrical energy is transferred. It can be expressed in three useful forms.
电功率是电能传递的速率，可用三种实用形式表示。
P = V × I P = I² × R P = V² / R
Power (P) is in watts (W). When choosing components, always check that the power rating is not exceeded.
功率（P）的单位是瓦特（W）。选用元件时，务必检查不要超过其额定功率。
8. Series and Parallel Circuits | 串联与并联电路
In a series circuit, the same current flows through all components. The total resistance is the sum of the individual resistances.
串联电路中，流过所有元件的电流相同，总电阻等于各电阻之和。
Rtotal = R₁ + R₂ + R₃ + …
The supply voltage is divided across the components in proportion to their resistances (voltage divider rule).
电源电压按各电阻的比例分配到各元件上（分压法则）。
In a parallel circuit, the total resistance is found using the reciprocal formula. Adding more branches decreases the overall resistance.
并联电路中，总电阻用倒数公式计算，增加支路会降低总电阻。
1 / Rtotal = 1 / R₁ + 1 / R₂ + 1 / R₃ + …
The voltage across each parallel branch is the same, while the total current splits among the branches (current divider).
各并联支路两端的电压相同，总电流则分配到各支路中（分流）。
9. Stress, Strain and Hooke’s Law | 应力、应变与胡克定律
When a material is loaded, it experiences stress and undergoes strain. Stress is the internal force per unit area, and strain is the resulting extension compared with the original length.
材料受载时会产生应力并发生应变。应力是单位面积上的内力，应变是伸长量与原长之比。
σ = F / A ε = ΔL / L₀
Stress (σ) is in pascals (Pa) or N/m²; strain (ε) has no units because it is a ratio.
应力（σ）的单位是帕斯卡（Pa）或 N/m²；应变（ε）为比值，无单位。
Hooke’s Law states that, for many materials, extension is proportional to the applied force, provided the elastic limit is not exceeded. The spring constant (k) describes the stiffness.
胡克定律指出：对许多材料而言，只要不超过弹性极限，伸长量与施加的力成正比。弹簧常数（k）描述刚度。
F = k × x
in the elastic region: E = σ / ε. It shows how easily a material stretches or compresses.
杨氏模量（E）将弹性区域内的应力与应变联系起来：E = σ / ε，它反映材料拉伸或压缩的难易程度。
10. Energy, Work and Power | 能量、功与功率
Work is done when a force moves an object. If the force and movement are in the same direction, work is simply force multiplied by distance.
当力使物体移动时便做功。若力与移动方向一致，功等于力乘以距离。
W = F × d
J). When lifting an object against gravity, the work done against the weight is m × g × h.
功和能量均以焦耳（J）为单位。将物体举高反抗重力做功时，做功大小为 m × g × h。
W = m × g × h
(g ≈ 9.8 N/kg on Earth, often approximated as 10 N/kg in class problems.)
（地球上的 g ≈ 9.8 N/kg，课堂练习中常取 10 N/kg。）
Power is the rate of doing work. A machine that does the same work in less time has a higher power.
功率是做功的快慢。在更短时间内完成同样功的机器功率更高。
P = W / t
/s. For a constant force moving at a steady speed, power can also be found with P = F × v.
功率以瓦特（W）为单位，1 W = 1 J/s。当恒力以稳定速度运动时，功率也可用 P = F × v 计算。
Conservation of energy reminds us that energy cannot be created or destroyed, only changed from one form to another – a principle that underpins all engineering systems.
能量守恒提醒我们：能量既不能创造也不能消灭，只能从一种形式转化为另一种——这是所有工程系统的基本原理。
Published by TutorHao | Engineering Revision Series | aleveler.com
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