📚 AS Edexcel Engineering Formula & Theorem Quick Reference Handbook | AS Edexcel 工程：公式定理速查手册
This quick reference handbook compiles the essential formulas, laws and theorems covered in the AS Edexcel Engineering specification. It serves as a rapid revision tool for students, linking core concepts from mechanics, materials, fluids, thermodynamics, electrical circuits and engineering mathematics. Each section presents key equations with brief explanations, helping you to apply them confidently in exam problem‑solving.
本速查手册汇编了 AS Edexcel 工程课程中的核心公式、定律与定理。它是一份快速复习工具，将力学、材料、流体、热力学、电路和工程数学中的基本概念联系起来。每个小节都列出关键方程并配以简要说明，帮助你在考试解题中从容运用。
1. Newton’s Laws of Motion | 牛顿运动定律
Newton’s first law states that an object remains at rest or in uniform motion unless acted upon by a resultant external force.
牛顿第一定律指出，物体将保持静止或匀速直线运动状态，除非受到合外力的作用。
Newton’s second law relates the resultant force to mass and acceleration.
牛顿第二定律将合力与质量和加速度联系起来。
F = m a
Newton’s third law states that for every action there is an equal and opposite reaction.
牛顿第三定律指出，每一个作用力都有一个大小相等、方向相反的反作用力。
Weight is the gravitational force acting on a mass near the Earth’s surface.
重量是地球表面附近作用在物体上的引力。
W = m g
The SI units: force in newtons (N), mass in kilograms (kg), acceleration in metres per second squared (m s⁻²), and g ≈ 9.81 m s⁻².
国际单位制单位：力为牛顿 (N)，质量为千克 (kg)，加速度为米每二次方秒 (m s⁻²)，g ≈ 9.81 m s⁻²。
2. Equilibrium and Moments | 平衡与力矩
A body is in translational equilibrium when the resultant force in any direction is zero.
当任意方向上的合力为零时，物体处于平动平衡状态。
ΣFx = 0, ΣFy = 0
Rotational equilibrium requires the sum of clockwise moments to equal the sum of anticlockwise moments about any pivot.
转动平衡要求绕任意支点的顺时针力矩之和等于逆时针力矩之和。
Σ Mclockwise = Σ Manticlockwise
The moment of a force is the product of the force and the perpendicular distance from the pivot.
力矩是力与从支点到力作用线的垂直距离的乘积。
M = F d
A couple consists of two equal and opposite parallel forces that produce pure rotation. The moment of a couple is the force multiplied by the perpendicular distance between the forces.
力偶由大小相等、方向相反且不共线的两个平行力构成，产生纯粹转动。力偶矩等于力乘以两力之间的垂直距离。
3. Stress, Strain and Young’s Modulus | 应力、应变与杨氏模量
Tensile or compressive stress is the force per unit cross‑sectional area.
拉伸或压缩应力是单位横截面积上的力。
σ = F / A
Tensile or compressive strain is the change in length divided by the original length.
拉伸或压缩应变是长度变化量除以原始长度。
ε = ΔL / L₀
Young’s modulus describes the stiffness of a material within its linear elastic region.
杨氏模量描述材料在线弹性范围内的刚度。
E = σ / ε
Engineering stress uses the original cross‑sectional area, while true stress uses the instantaneous area. For small strains in most structural metals, engineering stress is sufficiently accurate.
工程应力使用初始横截面积，而真实应力使用瞬时面积。对于大多数结构金属的小应变，工程应力足够精确。
4. Fluid Mechanics – Pressure and Bernoulli’s Principle | 流体力学 – 压强与伯努利原理
Pressure is defined as force per unit area acting normal to a surface.
压强定义为垂直作用在单位面积上的力。
P = F / A
In a static liquid, pressure increases with depth according to the hydrostatic equation.
在静止液体中，压强随深度增加，服从流体静力学方程。
P = ρ g h
For an incompressible, non‑viscous fluid flowing steadily, the continuity equation expresses conservation of mass.
对于不可压缩、无黏性流体的稳定流动，连续性方程体现了质量守恒。
A₁ v₁ = A₂ v₂
Bernoulli’s equation relates pressure, velocity and height along a streamline when flow is inviscid and incompressible.
伯努利方程描述了理想流体沿流线时压强、速度和高度之间的关系。
P + ½ ρ v² + ρ g h = constant
Volumetric flow rate is the product of cross‑sectional area and mean flow velocity, Q = A v.
体积流量是横截面积与平均流速的乘积，Q = A v。
5. Thermodynamics – Gas Laws and First Law | 热力学 – 气体定律与第一定律
The ideal gas law links pressure, volume, temperature and amount of substance.
理想气体状态方程联系了压强、体积、温度和物质的量。
p V = n R T
Boyle’s law states that for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume: p₁V₁ = p₂V₂.
波义耳定律指出，一定质量的气体在温度不变时，压强与体积成反比：p₁V₁ = p₂V₂。
Charles’s law shows that at constant pressure, volume is directly proportional to absolute temperature: V₁ / T₁ = V₂ / T₂.
查理定律表明，在压强不变时，体积与绝对温度成正比：V₁ / T₁ = V₂ / T₂。
The pressure law gives p₁ / T₁ = p₂ / T₂ for a constant‑volume process.
压力定律给出等容过程中 p₁ / T₁ = p₂ / T₂。
The first law of thermodynamics expresses energy conservation for a closed system.
热力学第一定律表达了封闭系统的能量守恒。
ΔU = Q − W
Here ΔU is the change in internal energy, Q is heat added to the system and W is work done by the system.
这里 ΔU 是内能变化量，Q 是系统吸收的热量，W 是系统对外做的功。
6. Electrical Circuits – Ohm’s Law, Power and Resistance | 电路 – 欧姆定律、功率与电阻
Ohm’s law defines the relationship between voltage, current and resistance at constant temperature.
欧姆定律定义了在恒定温度下电压、电流和电阻之间的关系。
V = I R
Electrical power is the rate at which energy is transferred in a circuit component.
电功率是电路元件中能量转移的速率。
P = I V = I² R = V² / R
Resistors in series add directly: Rtotal = R₁ + R₂ + R₃ + …
串联电阻直接相加：Rtotal = R₁ + R₂ + R₃ + …
For resistors in parallel, the reciprocal of the total resistance equals the sum of the reciprocals: 1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + …
对于并联电阻，总电阻的倒数等于各电阻倒数之和：1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + …
Kirchhoff’s current law (KCL) states that the sum of currents entering a junction equals the sum leaving. Kirchhoff’s voltage law (KVL) states that the algebraic sum of voltages around any closed loop is zero.
基尔霍夫电流定律 (KCL) 指出，流入节点的电流之和等于流出电流之和。基尔霍夫电压定律 (KVL) 指出，任一闭合回路中电压的代数和为零。
7. Kinematics – SUVAT Equations | 运动学 – SUVAT 方程
The SUVAT equations describe motion with constant acceleration along a straight line.
SUVAT 方程描述匀加速直线运动。
| s = displacement (m) | 位移 (m) |
| u = initial velocity (m s⁻¹) | 初速度 (m s⁻¹) |
| v = final velocity (m s⁻¹) | 末速度 (m s⁻¹) |
| a = constant acceleration (m s⁻²) | 恒定加速度 (m s⁻²) |
| t = time (s) | 时间 (s) |
The five equations are:
五个方程为：
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
s = ½ (u + v) t
s = v t − ½ a t²
These equations assume acceleration is constant and motion is in one dimension. For vertical motion under gravity, substitute a = −g.
这些方程假设加速度恒定且运动在一维方向上进行。对于重力作用下的竖直运动，代入 a = −g。
8. Work, Energy and Power | 功、能量与功率
Work is done when a force moves its point of application in the direction of the force.
当力的作用点沿力的方向发生位移时，力做功。
W = F s cos θ
Kinetic energy is the energy possessed by a body due to its motion.
动能是物体由于运动而具有的能量。
Ek = ½ m v²
Gravitational potential energy depends on height above a reference level.
重力势能取决于物体相对于参考平面的高度。
Ep = m g h
The work–energy principle states that the net work done on an object equals its change in kinetic energy.
功–能原理指出，作用在物体上的净功等于其动能的变化量。
Power is the rate of doing work or transferring energy.
功率是做功或能量转移的速率。
P = W / t = F v
Efficiency of a machine compares useful output power to input power: η = Pout / Pin.
机器的效率将有用输出功率与输入功率进行比较：η = Pout / Pin。
9. Material Properties – Hooke’s Law and Elasticity | 材料性能 – 胡克定律与弹性
Hooke’s law states that, within the elastic limit, extension is directly proportional to the applied load.
胡克定律指出，在弹性限度内，伸长量与所加载荷成正比。
F = k x
The spring constant k (N m⁻¹) measures stiffness. The elastic potential energy stored in a stretched spring or wire is given by:
弹簧常数 k (N m⁻¹) 度量刚度。储存在被拉伸的弹簧或金属丝中的弹性势能为：
Eelastic = ½ k x²
The limit of proportionality is the point beyond which Hooke’s law no longer applies. The elastic limit is the maximum stress a material can withstand without permanent deformation.
比例极限是胡克定律不再适用的点。弹性极限是材料能够承受而不发生永久变形的最大应力。
For a ductile material, the stress–strain curve shows a linear region, a yield point, plastic deformation and ultimate tensile strength before fracture.
对于延性材料，应力–应变曲线显示线弹性区、屈服点、塑性变形，以及断裂前的极限抗拉强度。
10. Friction and Inclined Planes | 摩擦与斜面
Friction opposes relative motion between two surfaces in contact. The maximum static friction is proportional to the normal reaction.
摩擦力阻碍接触面之间的相对运动。最大静摩擦力与法向反力成正比。
Fmax = μs R
Kinetic (sliding) friction is also proportional to the normal reaction but typically slightly smaller.
动（滑动）摩擦力也与法向反力成正比，但通常略小。
Fk = μk R
On an inclined plane, the weight mg is resolved into components parallel and perpendicular to the slope: mg sin θ down the plane and mg cos θ normal to the plane.
在斜面上，重力 mg 分解为平行于斜面的分量 mg sin θ 和垂直于斜面的分量 mg cos θ。
The coefficient of friction can be determined from the angle at which a block just begins to slide: μ = tan θ (when motion is impending on an incline).
摩擦系数可以通过物体刚开始滑动时的斜面倾角确定：μ = tan θ（当物体在斜面上即将运动时）。
11. Engineering Mathematics – Vectors and Trigonometry | 工程数学 – 矢量与三角学
A vector quantity has both magnitude and direction. Its components along perpendicular axes are found using trigonometry.
矢量既有大小又有方向。它沿相互垂直轴的分量可以使用三角学求得。
Fx = F cos θ, Fy = F sin θ
The magnitude of the resultant of two perpendicular components is given by Pythagoras’ theorem.
两个互相垂直分量的合矢量大小由勾股定理给出。
R = √(Fx² + Fy²)
The direction of the resultant is obtained from the tangent: tan θ = Fy / Fx.
合矢量的方向由正切函数得出：tan θ = Fy / Fx。
The sine rule and cosine rule are useful for non‑right‑angled triangles often encountered in force diagrams.
正弦定理和余弦定理常用于力多边形中非直角三角形的情况。
a / sin A = b / sin B = c / sin C
a² = b² + c² − 2 b c cos A
Moments and forces can be added using vector addition. In two dimensions, the polygon of forces provides a graphical method to determine an equilibrium resultant.
力矩和力可以用矢量加法合成。在二维情况下，力多边形提供了一种确定平衡合力的图形方法。
12. Dimensional Analysis | 量纲分析
Dimensional analysis uses the base quantities mass (M), length (L) and time (T) to check the consistency of engineering equations.
量纲分析利用基本量质量 (M)、长度 (L) 和时间 (T) 来检验工程方程的一致性。
Common derived dimensions include:
常见的导出量纲包括：
| Velocity, v | [L T⁻¹] |
| Acceleration, a | [L T⁻²] |
| Force, F | [M L T⁻²] |
| Pressure / Stress | [M L⁻¹ T⁻²] |
| Energy / Work / Torque | [M L² T⁻²] |
| Power | [M L² T⁻³] |
| Density, ρ | [M L⁻³] |
| Dynamic viscosity | [M L⁻¹ T⁻¹] |
An equation is dimensionally homogeneous if each term has the same base dimensions. For example, checking s = u t + ½ a t²: both sides give [L], confirming correctness.
如果一个方程各项具有相同的基本量纲，则该方程量纲齐次。例如，检验 s = u t + ½ a t²：左右两边都是 [L]，证实正确。
Dimensional analysis can also reveal relationships between physical quantities, though it cannot determine dimensionless constants.
量纲分析还可以揭示物理量之间的关系，但不能确定无量纲常数。
Published by TutorHao | Engineering Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导