📚 SQA Engineering: Formula and Theorem Quick Reference | SQA 工程：公式定理速查手册
This quick reference handbook provides a concise summary of essential formulae, laws, and theorems required for the SQA Higher Engineering Science course. It covers mechanics, electrical principles, analogue and digital electronics, materials, sensors, and control systems, helping you revise and apply key concepts effectively.
本速查手册简明总结了 SQA 高级工程科学课程所需的基本公式、定律和定理。内容涵盖力学、电学原理、模拟与数字电子学、材料、传感器和控制系统，帮助您有效复习和应用关键概念。
1. Linear Motion (Kinematics) | 直线运动（运动学）
Uniformly accelerated motion is described by four fundamental equations. These relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). They apply only when acceleration is constant.
匀加速运动由四个基本方程描述，它们关联位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t)。这些方程仅适用于加速度恒定的情况。
v = u + at
Equation (1) gives the final velocity after an interval of time t under constant acceleration.
方程 (1) 给出恒定加速度下经过时间 t 后的末速度。
s = ut + ½at²
Equation (2) calculates the displacement when initial velocity, time and constant acceleration are known.
方程 (2) 在已知初速度、时间和恒定加速度时计算位移。
v² = u² + 2as
Equation (3) links the square of the final velocity to the initial velocity, acceleration and displacement, without using time.
方程 (3) 将末速度的平方与初速度、加速度和位移联系起来，不涉及时间。
s = ½(u + v)t
Equation (4) expresses displacement as the average velocity multiplied by time. This is convenient when acceleration is not explicitly needed.
方程 (4) 将位移表示为平均速度乘以时间。当不需要直接使用加速度时，此式非常方便。
2. Forces and Newton’s Laws | 力与牛顿定律
Newton’s three laws form the foundation of mechanics. The first law introduces inertia; the second law quantifies the relationship between net force, mass and acceleration; the third law describes action–reaction pairs.
牛顿三定律构成了力学的基础。第一定律引入了惯性的概念；第二定律定量描述了净力、质量和加速度之间的关系；第三定律阐明了作用力与反作用力对。
F = ma
The net force F (in newtons, N) equals the mass m (kg) multiplied by the acceleration a (m/s²). Weight is a special case: W = mg, where g ≈ 9.8 m/s² on Earth.
净力 F（牛顿，N）等于质量 m（千克）乘以加速度 a（米/秒²）。重力是一个特例：W = mg，在地球表面 g ≈ 9.8 m/s²。
Newton’s third law reminds us that if body A exerts a force on body B, then B exerts an equal and opposite force on A; both forces are of the same type and act on different bodies.
牛顿第三定律指出，若物体 A 对物体 B 施加一个力，则 B 同时施加一个大小相等、方向相反的力于 A；这两个力属于同一类型，且作用在不同的物体上。
3. Energy and Power | 能量与功率
Work done by a constant force is the product of the force and the distance moved in the direction of the force. Energy is the capacity to do work, and both are measured in joules (J).
恒力所做的功等于力乘以沿力方向移动的距离。能量是做功的能力，两者均以焦耳 (J) 为单位。
W = Fd
If the force and displacement are not parallel, the component of force in the direction of motion must be used.
若力与位移不平行，则必须使用沿运动方向的力分量。
Kinetic Energy: KE = ½mv²
Gravitational Potential Energy: PE = mgh
Kinetic energy depends on mass and the square of speed. Gravitational potential energy near Earth’s surface depends on height h relative to a reference level.
动能取决于质量与速度的平方。地表附近的重力势能取决于相对于参考平面的高度 h。
Power: P = W / t = Fv
Power is the rate of doing work, measured in watts (W), where 1 W = 1 J/s. For a constant force moving at speed v, the useful power output is P = Fv.
功率是做功的速率，单位为瓦特 (W)，1 W = 1 J/s。对于以速度 v 运动的恒力，其有用功率输出为 P = Fv。
4. Moments and Static Equilibrium | 力矩与静力平衡
The turning effect of a force about a pivot is called the moment. Static equilibrium requires both translational and rotational balance.
力对支点的转动效应称为力矩。静力平衡要求同时满足平动平衡和转动平衡。
Moment = F × d
Here d is the perpendicular distance from the pivot to the line of action of the force. The moment is measured in newton‑metres (Nm).
其中 d 为支点到力作用线的垂直距离。力矩的单位是牛顿·米 (Nm)。
For an object in equilibrium, the sum of clockwise moments about any pivot equals the sum of anticlockwise moments, and the vector sum of all forces acting on the object is zero.
对于处于平衡状态的物体，对任意支点，顺时针力矩之和等于逆时针力矩之和，且作用于该物体的所有力的矢量和为零。
5. Materials: Stress, Strain and Young’s Modulus | 材料：应力、应变与杨氏模量
When a material is subjected to an external load, it deforms. Basic mechanical properties are described by stress, strain, and stiffness.
当材料承受外部载荷时会发生变形。基本的力学性能由应力、应变和刚度描述。
Stress: σ = F / A
Strain: ε = ΔL / L₀
Stress σ (N/m² or Pa) is the internal force per unit area. Strain ε (dimensionless) is the ratio of extension to original length L₀.
应力 σ（N/m² 或 Pa）是单位面积上的内力。应变 ε（无量纲）是伸长量 ΔL 与原长 L₀ 的比值。
Young’s modulus: E = σ / ε
Within the elastic limit, the stress–strain relationship is linear and the constant of proportionality is Young’s modulus E, which indicates the stiffness of a material.
在弹性极限内，应力—应变关系为线性，比例常数即为杨氏模量 E，它表征材料的刚度。
6. Basic Electrical Quantities and Ohm’s Law | 基本电学量与欧姆定律
Ohm’s law is the cornerstone of circuit analysis. It links voltage, current and resistance under constant temperature conditions.
欧姆定律是电路分析的基石。它在恒温条件下将电压、电流和电阻联系起来。
V = IR
Voltage V (volts) drives a current I (amperes) through a resistor R (ohms, Ω). The resistance restricts the flow of charge.
电压 V（伏特）驱动电流 I（安培）流过电阻 R（欧姆，Ω）。电阻限制电荷的流动。
Power in resistors: P = IV = I²R = V²/R
Electrical power (watts) can be calculated using any pair of I, V, and R. Resistors convert electrical energy into heat.
电功率（瓦特）可以利用 I、V、R 中的任意两个量计算。电阻将电能转化为热能。
Resistors in series: Rₜₒₜₐₗ = R₁ + R₂ + …
Resistors in parallel: 1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂ + …
Series resistances add directly; parallel resistances combine through the reciprocal rule, lowering the overall resistance.
串联电阻直接相加；并联电阻通过倒数规则组合，从而降低总电阻。
7. DC Circuit Analysis (Kirchhoff’s Laws) | 直流电路分析（基尔霍夫定律）
Kirchhoff’s laws are essential for analysing
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