📚 Year 10 WJEC Engineering: Formula and Theorem Quick Reference | Year 10 WJEC 工程公式定理速查手册
This quick reference handbook compiles the essential formulas and theorems needed for the WJEC Year 10 Engineering course. It covers mechanics, electronics, materials, and energy systems, giving you a rapid revision tool for tests and design tasks.
本速查手册汇编了 WJEC Year 10 工程课程所需的关键公式与定理，涵盖力学、电子学、材料与能量系统，为测验与设计任务提供快速复习工具。
1. Forces and Equilibrium | 力与平衡
Weight (Gravitational Force): The force on a mass due to gravity is W = m × g, where g ≈ 9.8 m/s² on Earth.
重量（重力）： 作用在物体上的重力为 W = m × g，地球表面 g ≈ 9.8 m/s²。
Newton’s Second Law: The resultant force on an object equals its mass multiplied by its acceleration: F = m × a.
牛顿第二定律： 作用在物体上的合力等于质量乘以加速度：F = m × a。
Equilibrium: For an object at rest or moving with constant velocity, the vector sum of all forces is zero: ΣF = 0.
平衡： 对于静止或匀速直线运动的物体，所有力的矢量和为零：ΣF = 0。
2. Moments and Levers | 力矩与杠杆
Moment of a Force: The turning effect about a pivot is M = F × d, where d is the perpendicular distance from the line of action to the pivot.
力矩： 绕支点的转动效果为 M = F × d，d 为力的作用线到支点的垂直距离。
Principle of Moments: For equilibrium, sum of clockwise moments = sum of anticlockwise moments (ΣMcw = ΣMacw).
力矩原理： 平衡时，顺时针力矩之和等于逆时针力矩之和（ΣMcw = ΣMacw）。
Lever Mechanical Advantage: For a simple lever, MA = Load / Effort (ideal case).
杠杆机械效益： 对于简单杠杆，MA = 负载 / 作用力（理想情况）。
3. Linear Motion | 直线运动
Average Speed: v = d / t, where d is distance travelled and t is time.
平均速度： v = d / t，d 为路程，t 为时间。
Acceleration: The rate of change of velocity: a = (v – u) / t, with u initial velocity, v final velocity.
加速度： 速度的变化率：a = (v – u) / t，u 为初速度，v 为末速度。
SUVAT Equations (constant acceleration): v = u + a t, s = u t + ½ a t², v² = u² + 2 a s.
匀加速运动方程： v = u + a t、s = u t + ½ a t²、v² = u² + 2 a s。
4. Work, Energy and Power | 功、能与功率
Work Done: When a force moves an object parallel to its line of action, W = F × d. Unit: joule (J).
做功： 力使物体沿其作用线方向移动时，W = F × d。单位：焦耳 (J)。
Kinetic Energy: KE = ½ m v², where m is mass and v is speed.
动能： KE = ½ m v²，m 为质量，v 为速度。
Gravitational Potential Energy: GPE = m × g × h, where h is height change.
重力势能： GPE = m × g × h，h 为高度变化。
Power: The rate of doing work: P = W / t. For constant velocity, P = F × v.
功率： 做功的速率：P = W / t。匀速运动时，P = F × v。
5. Mechanical Efficiency & Drive Systems | 机械效率与传动系统
Efficiency (η): η = (Useful output power / Total input power) × 100%. Always less than 1 due to friction.
效率 (η)： η =（有用输出功率 / 总输入功率）× 100%。因摩擦，总是小于 1。
Mechanical Advantage (MA) & Velocity Ratio (VR): MA = Load / Effort; VR = Distance moved by effort / Distance moved by load.
机械效益 (MA) 与速比 (VR)： MA = 负载 / 作用力；VR = 作用力移动距离 / 负载移动距离。
Link between efficiency: η = (MA / VR) × 100%.
效率关联： η = (MA / VR) × 100%。
Gear Ratio: For two meshing gears, Gear ratio = Number of teeth on driven gear / Number of teeth on driver gear = speed ratio.
齿轮比： 啮合齿轮，齿轮比 = 从动轮齿数 / 主动轮齿数，等于转速比。
6. Electrical Fundamentals | 电学基础
Charge: Q = I × t, where Q is charge (coulombs), I is current (amperes), t is time (seconds).
电荷： Q = I × t，Q 为电荷（库仑），I 为电流（安培），t 为时间（秒）。
Voltage (Potential Difference): V = W / Q, work done per unit charge.
电压（电势差）： V = W / Q，每单位电荷所做的功。
Ohm’s Law: At constant temperature, V = I × R, where R is resistance (ohms).
欧姆定律： 恒温时，V = I × R，R 为电阻（欧姆）。
Resistance in Series: R_total = R₁ + R₂ + …
串联电阻： R_total = R₁ + R₂ + …
Resistance in Parallel: 1
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