📚 Formula & Theorem Quick Reference for Year 11 Eduqas Engineering | Year 11 Eduqas 工程：公式定理速查手册
Mastering fundamental formulas and theorems is essential for success in Year 11 Eduqas Engineering. This quick reference handbook covers the key equations you need for mechanical systems, structures, electronics, and materials. Each entry provides clear definitions, typical units, and worked representations to help you apply them confidently in exams and coursework.
掌握基本公式和定理是 Year 11 Eduqas 工程学成功的关键。本速查手册涵盖了机械系统、结构、电子学和材料方面所需的关键方程。每个条目都提供了清晰的定义、常用单位以及示例表述，帮助你自信地在考试和课程作业中应用它们。
1. Mechanical Advantage (MA) and Velocity Ratio (VR) | 机械效益与速度比
) / Effort (input force). In an ideal system with no friction, MA equals Velocity Ratio (VR), which is the ratio of distance moved by effort to distance moved by load.
机械效益（MA）描述机构将输入力放大了多少。它是一个无量纲比值，定义为 MA = 负载（输出力） / 施力（输入力）。在理想无摩擦系统中，MA 等于速度比（VR），VR 是施力移动距离与负载移动距离之比。
MA = Load / Effort VR = Distance moved by effort / Distance moved by load
In real machines, friction reduces MA, so efficiency is always less than 100%.
在实际机械中，摩擦力会降低 MA，因此效率总是低于 100%。
2. Efficiency | 效率
Efficiency measures how well a system converts input energy into useful output work. It is expressed as a percentage using the formula:
效率衡量系统将输入能量转化为有用输出功的程度。用以下公式以百分比表示：
Efficiency (%) = (Useful output energy / Total input energy) × 100
ncy = (MA / VR) × 100. Always ensure the units for energy or work are consistent (joules).
另外，对于机械系统，效率也可以计算为 效率 = (MA / VR) × 100。务必确保能量或功的单位一致（焦耳）。
3. Gear Ratios | 齿轮比
A gear ratio determines the relationship between the speeds and torques of two connected gears. For two meshed gears, the gear ratio is the number of teeth on the driven gear divided by the number of teeth on the driver gear.
齿轮比决定两个相连齿轮的转速和扭矩之间的关系。对于两个啮合齿轮，齿轮比等于从动齿轮的齿数除以主动齿轮的齿数。
Gear Ratio = Number of teeth on driven gear / Number of teeth on driver gear
uces torque. The output speed can be found using: Output speed = Input speed / Gear Ratio.
比值大于 1 会降低转速但增加扭矩（扭矩倍增）；比值小于 1 会增加转速但降低扭矩。输出转速可通过下式求得：输出转速 = 输入转速 / 齿轮比。
4. Stress and Strain | 应力与应变
Stress (σ) is the internal force per unit area within a material when an external load is applied. It is measured in pascals (Pa) or N/m². Strain (ε) is the deformation per unit length – a dimensionless quantity that describes how much a material stretches or compresses relative to its original length.
应力（σ）是材料在承受外部载荷时单位面积上的内力。单位为帕斯卡（Pa）或 N/m²。应变（ε）是单位长度的变形量——一个无量纲量，描述材料相对于原始长度拉伸或压缩的程度。
oss-sectional area (A) Strain ε = Change in length (ΔL) / Original length (L)
Tensile stress tends to stretch the material; compressive stress tends to shorten it. Both are essential in structural analysis.
拉应力倾向于拉伸材料；压应力倾向于缩短材料。两者在结构分析中都至关重要。
5. Young's Modulus | 杨氏模量
Young's Modulus (E) is a measure of stiffness for an elastic material. It is the ratio of stress to strain within the material's elastic limit, where Hooke's law applies. A higher Young's Modulus indicates a stiffer material.
杨氏模量（E）是衡量弹性材料刚度的指标。它是材料在弹性极限内应力与应变之比，此时胡克定律适用。杨氏模量越高，材料越刚硬。
Young's Modulus (E) = Stress / Strain = (F/A) / (ΔL/L)
The unit is pascals (Pa). For example, mild steel has a Young's modulus of around 210 GPa, while aluminium is about 70 GPa.
单位为帕斯卡（Pa）。例如，低碳钢的杨氏模量约为 210 GPa，而铝约为 70 GPa。
6. Ohm's Law | 欧姆定律
Ohm's Law is the fundamental relationship in DC electrical circuits linking voltage (V), current (I), and resistance (R). It states that the current through a conductor is directly proportional to the voltage across it, provided temperature remains constant.
欧姆定律是直流电路中联系电压（V）、电流（I）和电阻（R）的基本关系。它指出，在温度保持恒定的条件下，通过导体的电流与导体两端的电压成正比。
× R Voltage (V) in volts, Current (I) in amperes, Resistance (R) in ohms (Ω)
s law is used for analysing sensors, selecting resistors, and designing simple control circuits.
可重新整理为 I = V / R 或 R = V / I。该定律用于分析传感器、选择电阻器以及设计简单的控制电路。
7. Power in Electrical Circuits | 电路中的功率
Electrical power (P) is the rate at which energy is transferred in a circuit. It can be calculated using voltage and current, or by combining Ohm's law to account for resistance.
电功率（P）是电路中的能量传递速率。可以使用电压和电流计算，或结合欧姆定律考虑电阻来计算。
P = V × I P = I² × R P = V² / R
Power is measured in watts (W). In practical engineering, knowing power helps select components with appropriate ratings (e.g., resistor power rating, motor wattage).
功率以瓦特（W）为单位。在实际工程中，了解功率有助于选择具有适当额定值的元件（例如电阻器额定功率、电机功率）。
8. Resistors in Series and Parallel | 串联与并联电阻
When resistors are connected in series, the total resistance is the sum of individual resistances. In parallel, the total resistance is found by taking the reciprocal of the sum of reciprocals.
电阻串联时，总电阻等于各个电阻之和。并联时，总电阻等于各电阻倒数之和的倒数。
Series: Rtotal = R₁ + R₂ + R₃ + ...
Parallel: 1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + ...
For two parallel resistors, the simplified form is Rtotal (R₁ × R₂) / (R₁ + R₂). These rules help in designing voltage dividers and sensor networks.
对于两个并联电阻，简化公式为 Rtotal = (R₁ × R₂) / (R₁ + R₂)。这些规则有助于设计分压器和传感器网络。
9. Moments and Equilibrium | 力矩与平衡
A moment is the turning effect of a force about a pivot. It is defined as the product of the force and the perpendicular distance from the line of action of the force to the pivot.
力矩是力绕支点产生的转动效应。其定义为力与从力的作用线到支点的垂直距离的乘积。
Moment = Force × Perpendicular distance from pivot
The principle of moments states that for a system in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments. This is vital for analysing levers, bridges, and crane structures.
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。这对于分析杠杆、桥梁和起重机结构至关重要。
10. Work, Energy and Power in Mechanical Systems | 机械系统中的功、能与功率
Work done (W) is the energy transferred when a force moves an object. It is calculated as force multiplied by distance moved in the direction of the force. Power (P) is the rate of doing work.
做功（W）是力使物体移动时传递的能量。它等于力乘以物体在力的方向上移动的距离。功率（P）是做功的速率。
Work done W = F × d Power P = W / t = (F×d) / t
rth), and h is height. Kinetic energy (KE) is KE = ½ × m × v². All energies are measured in joules (J), power in watts (W).
提升物体获得的重力势能（GPE）为 GPE = m × g × h，其中 m 为质量，g 为重力场强度（地球约 10 N/kg），h 为高度。动能（KE）为 KE = ½ × m × v²。所有能量的单位为焦耳（J），功率的单位为瓦特（W）。
11. Density | 密度
Density (ρ) is mass per unit volume of a substance. It is a key material property used to estimate weight, select materials for lightweight designs, and calculate buoyancy.
密度（ρ）是物质单位体积的质量。它是一个关键的材料属性，用于估算重量、选择轻量化设计材料以及计算浮力。
Density ρ = Mass (m) / Volume (V)
Typical units are kg/m³ or g/cm³. For example, the density of water is 1000 kg/m³, aluminium about 2700 kg/m³, and steel about 7800 kg/m³.
典型单位是 kg/m³ 或 g/cm³。例如，水的密度为 1000 kg/m³，铝约 2700 kg/m³，钢约 7800 kg/m³。
12. Pressure | 压力
Pressure (p) is the force acting perpendicularly per unit area. In hydraulic systems, a small input force can produce a large output force because pressure is transmitted equally throughout an enclosed fluid.
压强（p）是垂直作用在单位面积上的力。在液压系统中，由于密封流体中的压强处处相等地传递，较小的输入力可以产生较大的输出力。
Pressure p = Force (F) / Area (A)
. Pressure is measured in pascals (Pa). For hydraulic advantage, p₁ = p₂ so F₁/A₁ = F₂/A₂.
这一原理是液压千斤顶、制动系统和气动控制的基础。压强以帕斯卡（Pa）为单位。对于液压增益，p₁ = p₂，因此 F₁/A₁ = F₂/A₂。
Published by TutorHao | Engineering Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图