📚 Year 9 Edexcel Engineering Formula & Theorem Quick Reference Handbook | 九年级爱德思工程公式定理速查手册
This quick reference handbook compiles the essential formulas and theorems covered in the Year 9 Edexcel Engineering curriculum. It provides clear statements of each principle, the relevant mathematical expression, and short explanations to help you revise key concepts in mechanics, electricity, materials and energy. Having these equations at your fingertips will strengthen your problem-solving skills and prepare you for both written assessments and practical design challenges.
本速查手册汇集了九年级爱德思工程课程中的核心公式与定理。每个原理都配有清晰的表述、相关的数学表达式和简要解释，帮助你复习力学、电学、材料和能量等关键概念。熟悉这些方程将提升你解决问题的能力，为笔试和实际工程设计挑战做好准备。
1. Force and Newton’s Laws | 力与牛顿定律
Newton’s Second Law of Motion states that the net force acting on an object is equal to the product of its mass and acceleration. This relationship is fundamental to all dynamic systems in engineering, from vehicle design to structural loading.
牛顿第二运动定律指出，作用在物体上的合力等于其质量与加速度的乘积。这一关系是车辆设计到结构负载等所有工程动态系统的基础。
F = m × a
Weight is the force exerted by gravity on a mass. On Earth, the gravitational field strength g is approximately 9.8 m/s², often rounded to 10 m/s² for simple calculations.
重量是重力施加在质量上的力。在地球上，重力场强 g 约为 9.8 m/s²，为简化计算常取 10 m/s²。
W = m × g
For an object in equilibrium (at rest or moving at constant velocity), the resultant force is zero. In a free-body diagram, all forces can be resolved, and the vector sum in any direction equals zero.
处于平衡状态（静止或匀速运动）的物体，其合力为零。在受力分析图中，可以分解所有力，任何方向的矢量和都等于零。
ΣF = 0
2. Moments and Levers | 力矩与杠杆原理
The turning effect of a force is called a moment. It depends on the magnitude of the force and the perpendicular distance from the pivot to the line of action of the force.
力的转动效应称为力矩。它取决于力的大小以及从支点到力作用线的垂直距离。
Moment = F × d
The principle of moments states that for a system in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about the same pivot. This is used to calculate unknown forces in levers and beams.
力矩原理指出，对于转动平衡的系统，顺时针力矩的总和等于逆时针力矩的总和（绕同一支点）。该原理用于计算杠杆和梁中的未知力。
Σ clockwise moments = Σ anticlockwise moments
Levers are classified into three types depending on the relative positions of the fulcrum, load and effort. The mechanical advantage of a lever can be expressed as the ratio of load to effort.
杠杆根据支点、负载和施力点的相对位置分为三类。杠杆的机械利益可表示为负载与施力的比值。
MA = Fload / Feffort
3. Work, Energy and Power | 功、能量与功率
Work is done when a force moves an object through a distance in the direction of the force. The unit of work is the joule (J).
当力使物体在力的方向上移动一段距离时，力对物体做功。功的单位是焦耳 (J)。
W = F × d
Kinetic energy is the energy an object possesses due to its motion. It increases with mass and the square of velocity, making speed a critical factor in crash safety design.
动能是物体因其运动而具有的能量。它与质量和速度的平方成正比，因此速度是碰撞安全设计中的关键因素。
KE = ½ × m × v²
Gravitational potential energy is stored in an object raised above a reference level. It is a form of mechanical energy that can be converted into kinetic energy, as in roller coasters and hydroelectric dams.
重力势能是物体被提升到参考水平面以上时储存的能量。它是一种可以转化为动能的机械能，例如在过山车和水力发电大坝中。
GPE = m × g × h
Power measures the rate at which work is done or energy is transferred. A machine that does the same work in less time has greater power.
功率衡量做功或能量转换的速率。能在更短时间内完成同样功的机器功率更大。
P = W / t
4. Efficiency and Mechanical Advantage | 效率与机械利益
Efficiency compares the useful output of a system to its total input. It is always less than 100% due to friction, heat loss and other dissipative effects.
效率将系统的有用输出与总输入进行比较。由于摩擦、热量损失和其他耗散效应，效率总是低于 100%。
Efficiency = (useful output energy / total input energy) × 100%
In terms of power, efficiency can also be written using power values. This form is useful for motors and engines where power ratings are given.
用功率表示时，效率也可写成如下形式。这种形式适用于给出额定功率的电动机和发动机。
Efficiency = (useful power output / total power input) × 100%
Mechanical advantage (MA) is the factor by which a mechanism multiplies the force put into it. For an ideal machine, MA equals the velocity ratio (VR), but in practice MA is lower.
机械利益 (MA) 表示机构将输入力放大的倍数。对于理想机械，MA 等于速度比 (VR)，但实际上 MA 较小。
MA = Fₗ / Fₑ
Velocity ratio is the ratio of the distance moved by the effort to the distance moved by the load in the same time. For lever and pulley systems, it depends on geometry.
速度比是在相同时间内施力端移动距离与负载端移动距离的比值。对于杠杆和滑轮系统，它取决于几何结构。
VR = dₑ / dₗ
The efficiency of a machine can also be found from the mechanical advantage and velocity ratio.
机械效率也可通过机械利益和速度比求得。
Efficiency = (MA / VR) × 100%
5. Basic Electrical Laws | 基础电学定律
Ohm’s Law relates voltage (V), current (I) and resistance (R) in a conductor at constant temperature. It is the cornerstone of circuit analysis in electronic and electrical engineering.
欧姆定律描述了在恒定温度下导体中电压 (V)、电流 (I) 和电阻 (R) 之间的关系。它是电子与电气工程中电路分析的基础。
V = I × R
Electrical power is the product of voltage and current. High-power devices draw large currents or operate at high voltages, which influences wiring and safety design.
电功率是电压和电流的乘积。大功率设备会吸入大电流或在高压下运行，这会影响布线和安全设计。
P = V × I
Electric charge (Q) is the amount of electricity transferred by a steady current over time. It is measured in coulombs (C).
电荷量 (Q) 是恒定电流在一段时间内传输的电量，单位为库仑 (C)。
Q = I × t
Electrical energy consumed can be expressed as the product of power and time, or using voltage, current and time. This is the basis of kilowatt-hour metering.
消耗的电能可以表示为功率与时间的乘积，也可表示为电压、电流和时间的乘积。这是千瓦时计量的基础。
E = P × t = V × I × t
6. Resistance and Circuits | 电阻与电路
Resistors in series increase the total resistance because the current must pass through each resistor sequentially. The equivalent resistance is the sum of individual resistances.
串联的电阻会增加总电阻，因为电流必须依次流过每个电阻。等效电阻为各个电阻之和。
Rₜ = R₁ + R₂ + R₃ + …
Resistors in parallel provide multiple paths for current, reducing the total resistance. The reciprocal of total resistance equals the sum of the reciprocals of individual resistances.
并联电阻为电流提供多条路径，降低了总电阻。总电阻的倒数等于各个电阻倒数之和。
1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃ + …
For exactly two resistors in parallel, a simplified product-over-sum formula can be used. This is a quick calculation for branching circuits with two loads.
对于恰好两个电阻并联的情况，可以使用简化的积除以和公式。这是计算有两个负载的分支电路的快捷方法。
Rₜ = (R₁ × R₂) / (R₁ + R₂)
In all resistive circuits, Ohm’s Law and the power formulas remain valid, but the correct total resistance must be found first.
在所有电阻电路中，欧姆定律和功率公式仍然有效，但必须首先求出正确的总电阻。
7. Mechanical Properties of Materials | 材料的力学性能
Density is mass per unit volume, an important property for material selection in lightweight structures and buoyancy calculations.
密度是单位体积的质量，是轻量化结构和浮力计算中选材的重要属性。
ρ = m / V
Pressure quantifies the normal force acting per unit area. It is crucial in hydraulic systems, pneumatics and assessing how loads are distributed across surfaces.
压强量化了作用在单位面积上的法向力。它在液压系统、气动系统以及评估负载在表面上的分布中至关重要。
p = F / A
Hooke’s Law describes the linear elastic behaviour of springs and many engineering materials within their elastic limit. The spring constant k measures stiffness.
胡克定律描述了弹簧和许多工程材料在弹性极限内的线性弹性行为。弹簧常数 k 衡量刚度。
F = k × x
8. Stress, Strain and Young’s Modulus | 应力、应变与杨氏模量
Stress is the internal force per unit cross-sectional area within a material subjected to tension or compression. It has the same units as pressure, pascals (Pa).
应力是材料在承受拉伸或压缩时，单位横截面积上的内力，其单位与压强相同，为帕斯卡 (Pa)。
σ = F / A
Strain is the dimensionless ratio of the change in length to the original length. It indicates how much a material deforms under load.
应变是长度变化量与原始长度的无量纲比值，表示材料在载荷下的变形程度。
ε = ΔL / L₀
Young’s modulus (E) is a measure of a material’s stiffness, defined as the ratio of stress to strain in the linear-elastic region of the stress-strain curve.
杨氏模量 (E) 是衡量材料刚度的量度，定义为应力-应变曲线线性弹性区域内应力与应变之比。
E = σ / ε
9. Heat Transfer and Energy | 热传递与能量
The energy needed to change the temperature of a substance depends on its mass, specific heat capacity and the temperature change. This formula is fundamental in thermal system design.
改变物质温度所需的能量取决于其质量、比热容和温度变化。该公式是热系统设计的基础。
Q = m × c × Δθ
Heat transfer occurs by conduction, convection and radiation. In many Year 9 problems, conduction through solids is approximated by a steady-state rate equation, but the principle of energy conservation is always applied.
热传递通过传导、对流和辐射进行。在九年级的许多问题中，固体中的热传导常近似为稳态速率方程，但能量守恒原理始终适用。
Energy conservation (first law of thermodynamics) states that energy cannot be created or destroyed, only transferred or converted from one form to another. This underpins all efficiency calculations.
能量守恒（热力学第一定律）指出，能量不能被创造或消灭，只能从一种形式转移到另一种形式或转换为其他形式。这是所有效率计算的基础。
Ein = Eout + Eloss
10. Gears, Pulleys and Transmission | 齿轮、滑轮与传动
Gear ratio is defined as the ratio of the number of teeth on the driven gear to the number of teeth on the driver gear. A ratio greater than one indicates speed reduction and torque increase.
齿轮比定义为从动齿轮齿数与主动齿轮齿数之比。比值大于 1 表示减速和扭矩增大。
Gear ratio = N₂ / N₁
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