📚 Year 12 WJEC Engineering: Formula & Theorem Quick Reference Handbook | 工程公式定理速查手册
This quick reference handbook compiles the essential formulas, laws, and theorems that underpin Year 12 WJEC Engineering. Covering mechanics, materials, fluids, thermodynamics, electronics, digital logic, and mathematics, each entry is paired with a concise explanation in both English and Chinese. Use it to reinforce your understanding, solve problems efficiently, and build a solid foundation for the exam.
本速查手册汇编了 WJEC 工程学 Year 12 所依据的核心公式、定律和定理。内容涵盖力学、材料、流体、热力学、电子学、数字逻辑和数学，每一条目都配有中英文简明解释。可用于巩固理解、高效解题，并为考试打下扎实基础。
1. Kinematics & Dynamics | 运动学与动力学
Uniformly accelerated motion is described by the SUVAT equations, where u = initial velocity, v = final velocity, a = constant acceleration, t = time, s = displacement.
匀加速运动由 SUVAT 方程描述，u = 初速度，v = 末速度，a = 恒定加速度，t = 时间，s = 位移。
v = u + a t — calculates final velocity without displacement.
v = u + a t — 在不涉及位移时计算末速度。
s = u t + ½ a t² — finds displacement when final velocity is not known.
s = u t + ½ a t² — 当未知末速度时求位移。
v² = u² + 2 a s — relates velocities and displacement without time.
v² = u² + 2 a s — 关联速度和位移，无需时间。
s = ½ (u + v) t — average velocity form for displacement.
s = ½ (u + v) t — 使用平均速度求位移。
Newton’s Second Law and momentum complete the dynamic picture.
牛顿第二定律和动量完善了动力学图景。
ΣF = m a — net force equals mass times acceleration.
ΣF = m a — 合力等于质量乘以加速度。
p = m v — linear momentum.
p = m v — 线动量。
Impulse = F Δt = Δp — impulse–momentum theorem.
冲量 = F Δt = Δp — 冲量‑动量定理。
2. Forces, Moments & Equilibrium | 力、力矩与平衡
A body is in static equilibrium when the resultant force and resultant moment about any point are both zero.
当物体所受的合外力以及对任意点的合力矩均为零时，物体处于静力平衡。
ΣFₓ = 0, ΣF_y = 0, ΣF_z = 0 — translational equilibrium.
ΣFₓ = 0, ΣF_y = 0, ΣF_z = 0 — 平动平衡条件。
ΣM = 0 — rotational equilibrium: sum of clockwise moments = sum of anticlockwise moments about any pivot.
ΣM = 0 — 转动平衡：对任意支点，顺时针力矩之和等于逆时针力矩之和。
M = F × d — moment of a force about a point (d is the perpendicular distance from the line of action to the pivot).
M = F × d — 力对一点的力矩（d 为力的作用线到支点的垂直距离）。
F_f ≤ μ R — limiting friction (μ: coefficient of friction, R: normal reaction force).
F_f ≤ μ R — 极限摩擦力（μ：摩擦系数，R：法向反力）。
3. Work, Energy & Power | 功、能与功率
These relationships govern energy transfer in mechanical systems and are fundamental for efficiency calculations.
以下关系式支配着机械系统中的能量传递，是效率计算的基础。
W = F s cos θ — work done by a constant force (θ: angle between force and displacement).
W = F s cos θ — 恒力做功（θ 为力与位移的夹角）。
KE = ½ m v² — translational kinetic energy.
KE = ½ m v² — 平动动能。
GPE = m g h — gravitational potential energy near Earth’s surface (g ≈ 9.81 m s⁻²).
GPE = m g h — 地球表面附近的重力势能（g ≈ 9.81 m s⁻²）。
P = W / t = F v — average power (left) and instantaneous power for a force acting along the direction of velocity.
P = W / t = F v — 平均功率（左）以及力沿速度方向的瞬时功率。
E_initial = E_final (if no work done by external non‑conservative forces) — conservation of mechanical energy.
E_初始 = E_最终（若无外部非保守力做功）— 机械能守恒。
4. Stress, Strain & Young’s Modulus | 应力、应变与杨
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