📚 A-Level CCEA Engineering: Quick Reference Formula & Theorem Handbook | A-Level CCEA 工程：公式定理速查手册
This quick reference handbook compiles the essential formulas, theorems, and constants required for the CCEA GCE Engineering specification. It covers mechanics, materials, electrical circuits, thermodynamics, and fluids, providing a single source for revision and problem-solving.
本速查手册汇编了 CCEA GCE 工程学规范所必需的核心公式、定理和常数。内容涵盖力学、材料、电路、热力学和流体，为复习和解题提供一站式参考。
1. Linear Motion (SUVAT) | 直线运动 (SUVAT)
When an object moves with uniform acceleration in a straight line, its motion can be described by five interrelated quantities and four fundamental equations, often referred to as the SUVAT equations. The symbols are: s – displacement (m), u – initial velocity (m/s), v – final velocity (m/s), a – acceleration (m/s²), t – time (s).
当物体沿直线做匀加速运动时，其运动可由五个相关联的物理量和四个基本方程描述，通常称为 SUVAT 方程。符号：s – 位移 (m)、u – 初速度 (m/s)、v – 末速度 (m/s)、a – 加速度 (m/s²)、t – 时间 (s)。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
Equation (1) links final velocity, initial velocity, and acceleration. Equation (2) gives displacement when initial velocity and time are known. Equation (3) is useful when time is not given. Equation (4) calculates displacement from the average velocity.
方程(1)联系了末速度、初速度和加速度。方程(2)在已知初速度和时间时给出位移。方程(3)在未给出时间时有用。方程(4)利用平均速度计算位移。
2. Newton's Laws and Forces | 牛顿定律与力
Newton's three laws of motion govern the relationship between forces and motion. The first law states that an object remains at rest or in uniform motion unless acted upon by a resultant force. The second law quantifies force as the product of mass and acceleration. The third law asserts that forces occur in equal and opposite pairs.
牛顿三大运动定律支配力与运动的关系。第一定律指出，除非受到合外力作用，物体将保持静止或匀速直线运动。第二定律将力量化为质量与加速度的乘积。第三定律指出，力成对出现且大小相等、方向相反。
F = ma
ass (kg), a is acceleration (m/s²). Weight is a special force: W = mg, with g = 9.81 m/s².
其中 F 为合外力 (N)，m 为质量 (kg)，a 为加速度 (m/s²)。重力是一种特殊的力：W = mg，g = 9.81 m/s²。
For equilibrium, the vector sum of forces must be zero: ΣF = 0. Friction Ff ≤ μR, where μ is the coefficient of friction and R is the normal reaction.
平衡状态下，力的矢量和必须为零：ΣF = 0。摩擦力 Ff ≤ μR，其中 μ 为摩擦系数，R 为法向反作用力。
3. Moments and Torque | 力矩与扭矩
The moment of a force about a pivot is the product of the force and the perpendicular distance from the pivot to the line of action of the force. Torque is a rotational analogue of force.
力对支点的力矩是力的大小与支点到力作用线的垂直距离的乘积。扭矩是力的旋转类比。
M = F × d
where M is the moment (Nm), F is the force (N), and d is the perpendicular distance (m). The principle of moments states that for a system in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.
其中 M 为力矩 (Nm)，F 为力 (N)，d 为垂直距离 (m)。力矩原理指出，对于处于转动平衡的系统，顺时针力矩之和等于逆时针力矩之和。
4. Work, Energy and Power | 功、能量与功率
Work is done when a force moves its point of application. Energy is the capacity to do work. Power is the rate of doing work or transferring energy.
当力使其作用点移动时做功。能量是做功的能力。功率是做功或能量转移的速率。
W = Fs cosθ
Ek = ½mv²
Ep = mgh
P = W / t = Fv
where W is work (J), F is force (N), s is displacement (m), θ is the angle between force and displacement. Kinetic energy Ek = ½mv². Gravitational potential energy Ep height). Power P (W) equals work done per unit time or the product of force and velocity.
其中 W 为功 (J)，F 为力 (N)，s 为位移 (m)，θ 为力与位移的夹角。动能 Ek = ½mv²。重力势能 Ep = mgh (h 为高度)。功率 P (W) 等于单位时间所做的功或力与速度的乘积。
5. Stress, Strain and Young's Modulus | 应力、应变与杨氏模量
When a material is subjected to a tensile or compressive force, it experiences stress and strain. Hooke's law applies within the elastic limit.
当材料承受拉伸或压缩力时，会产生应力和应变。胡克定律适用于弹性极限内。
Stress σ = F / A
Strain ε = ΔL / L₀
Young's Modulus E = σ / ε
Factor of Safety = Ultimate tensile strength /
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