📚 Year 11 WJEC Engineering Formula & Theorem Quick Reference Handbook | Year 11 WJEC 工程公式定理速查手册
This handbook brings together essential formulas, theorems and key quantitative relationships for the Year 11 WJEC Engineering syllabus. Use it to test your recall, check numerical answers and build confidence in applying principles from mechanics, materials and electrical systems.
本手册汇集了 Year 11 WJEC 工程课程的核心公式、定理和关键数量关系。你可以用它检验记忆、核对计算结果，并在力学、材料与电学系统的应用中建立信心。
1. Mechanical Advantage & Velocity Ratio | 机械利益与速度比
Mechanical Advantage (MA) tells you how many times a mechanism multiplies the input effort. It is the ratio of load to effort.
机械利益（MA）表示机构将输入作用力放大的倍数，定义为负载与作用力之比。
MA = Load ÷ Effort
Velocity Ratio (VR) compares the distance moved by the effort to the distance moved by the load. For an ideal frictionless machine, MA = VR.
速度比（VR）比较作用力移动距离与负载移动距离的比值。对于无摩擦的理想机械，MA = VR。
VR = Distance moved by effort ÷ Distance moved by load
2. Forces, Moments & Equilibrium | 力、力矩与平衡
A moment is the turning effect of a force. For equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments about any pivot.
力矩是力的转动效果。在平衡状态下，绕任何支点，顺时针力矩之和等于逆时针力矩之和。
Moment (M) = Force (F) × Perpendicular distance (d)
Σ Mclockwise = Σ Manticlockwise
When a beam or lever is in equilibrium, the upward forces equal the downward forces (no resultant force).
当梁或杠杆平衡时，向上的力等于向下的力（合力为零）。
3. Stress, Strain & Hooke’s Law | 应力、应变与胡克定律
Stress measures the internal force acting per unit area inside a material. Strain measures the fractional change in length.
应力衡量材料内部单位面积上作用的力。应变衡量长度的相对变化。
Stress (σ) = Force (F) ÷ Cross-sectional area (A)
Strain (ε) = Extension (ΔL) ÷ Original length (L₀)
Hooke’s Law states that, within the elastic limit, extension is directly proportional to the applied force.
胡克定律指出，在弹性限度内，伸长量与施加的力成正比。
F = k × x
where k is the spring constant (stiffness) and x is the extension.
其中 k 为劲度系数（弹簧常数），x 为伸长量。
4. Young’s Modulus | 杨氏模量
Young’s Modulus (E) describes the stiffness of a material. It is the gradient of the stress–strain graph in the linear region.
杨氏模量（E）描述材料的刚度，是应力-应变图在线性区域的斜率。
E = Stress ÷ Strain = (F/A) ÷ (ΔL/L₀)
A stiffer material has a higher Young’s Modulus. The unit is pascal (Pa) or N/m².
刚度越大的材料杨氏模量越高。单位为帕斯卡（Pa）或 N/m²。
5. Work, Energy & Power | 功、能量与功率
Work done by a constant force equals the force multiplied by the distance moved in the direction of the force.
恒力所做的功等于力乘以在该力方向上移动的距离。
Work (W) = Force (F) × Distance (d)
Power is the rate of doing work. It can also be expressed as force times velocity.
功率是做功的快慢，也可表示为力乘以速度。
Power (P) = Work ÷ Time = W/t = F × v
Kinetic energy and gravitational potential energy are important in analysis of moving systems.
动能和重力势能在分析运动系统时很重要。
Ek = ½ m v² Ep = m g h
6. Efficiency | 效率
Efficiency measures how well a system converts input energy into useful output. It is always less than 100% because of friction and heat losses.
效率衡量系统将输入能量转化为有用输出的程度。由于摩擦和热量损失，它总小于 100%。
Efficiency (η) = (Useful output energy ÷ Total input energy) × 100%
In mechanical systems, efficiency can also be found from MA and VR: η = (MA ÷ VR) × 100%.
在机械系统中，效率也可通过 MA 和 VR 求得：η = (MA ÷ VR) × 100%。
7. Kinematic Equations (SUVAT) | 运动学方程 (SUVAT)
These equations describe motion with uniform acceleration in a straight line. The symbols are: s – displacement, u – initial velocity, v – final velocity, a – acceleration, t – time.
这些方程描述匀加速直线运动。符号含义：s – 位移，u – 初速度，v – 末速度，a – 加速度，t – 时间。
v = u + a t
s = u t + ½ a t²
v² = u² + 2 a s
s = ½ (u + v) t
8. Ohm’s Law & Electrical Power | 欧姆定律与电功率
Ohm’s Law relates potential difference, current and resistance in a metallic conductor at constant temperature.
欧姆定律描述了在恒温下金属导体中电压、电流与电阻的关系。
V = I × R
Electrical power and energy dissipation can be calculated from current and voltage.
电功率和能量耗散可通过电流和电压计算。
P = V × I = I² × R = V² ÷ R
Always select the most convenient form when two quantities are known.
当已知两个量时，选择最便捷的形式计算。
9. Fluid Pressure & Hydraulic Systems | 流体压力与液压系统
The pressure exerted by a column of liquid depends on density, gravitational field strength and vertical height.
液柱产生的压强取决于液体密度、重力场强度和垂直高度。
p = ρ × g × h
In a hydraulic system, pressure is transmitted undiminished throughout an enclosed fluid. This principle is used to multiply force.
在液压系统中，压强在封闭液体中大小不变地向各个方向传递，这一原理用于放大力。
p = F₁ ÷ A₁ = F₂ ÷ A₂
The force multiplication factor equals the ratio of the piston areas.
力放大倍数等于活塞面积之比。
10. Gear & Pulley Ratios | 齿轮比与滑轮比
Gear ratio is determined by the number of teeth on meshing gears. It governs the speed and torque transformation.
齿轮比由啮合齿轮的齿数决定，决定转速和转矩的转换。
Gear Ratio = Ndriven ÷ Ndriver = ωdriver ÷ ωdriven
For a simple pulley system, velocity ratio is the number of rope sections supporting the load, assuming negligible friction.
对于简单滑轮系统，速度比等于支持负载的绳索段数（忽略摩擦）。
11. Levers: Classes & Mechanical Advantage | 杠杆：类别与机械利益
Levers are categorised by the relative positions of the effort, load and fulcrum (pivot). In all types, the principle of moments applies.
杠杆根据作用力、负载和支点的相对位置分类。所有类型都适用力矩原理。
Load × Load arm = Effort × Effort arm
Thus, MA can also be expressed in terms of the effort arm and load arm.
因此 MA 也可用力臂的长度比来表示。
MA = Effort arm ÷ Load arm
- Class 1: Fulcrum between effort and load (e.g. seesaw)
- 一类杠杆：支点在作用力与负载之间（如跷跷板）
- Class 2: Load between fulcrum and effort (e.g. wheelbarrow)
- 二类杠杆：负载在支点与作用力之间（如手推车）
- Class 3: Effort between fulcrum and load (e.g. tweezers)
- 三类杠杆：作用力在支点与负载之间（如镊子）
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