📚 Quick Reference Handbook for Edexcel Engineering Year 10: Formulas & Theorems | Year 10 Edexcel 工程：公式定理速查手册
This quick reference handbook brings together the essential formulas and theorems you need to master for the Year 10 Edexcel Engineering course. It covers core topics from mechanics, electricity, energy, and materials science, presented in a clear and exam-focused way. Use it for revision, homework support, or quick checks during practical work. Each formula is accompanied by a concise explanation in both English and Chinese, helping you to understand not only how to apply it, but also what it means in engineering contexts.
本速查手册汇总了 Year 10 Edexcel 工程课程必须掌握的关键公式和定理，涵盖力学、电学、能量和材料科学等核心主题。每一条公式都配有中英双语讲解，既适合考前复习，也可用于日常作业与实验快速查阅。理解公式背后的工程意义，能让你在答题和解决实际问题时更有把握。
1. Newton's Second Law of Motion | 牛顿第二运动定律
Newton's Second Law relates the net force acting on an object to its mass and acceleration. The formula is fundamental to understanding how objects move and respond to forces in all branches of engineering.
牛顿第二定律将物体所受合外力与其质量和加速度联系起来，是理解所有工程领域中物体如何运动和受力响应的基础。
F = m × a
Where F is the net force in newtons (N), m is the mass in kilograms (kg), and a is the acceleration in metres per second squared (m/s²). A larger force produces a larger acceleration, and a larger mass reduces the acceleration for the same force.
其中 F 是合外力（单位：牛顿 N），m 是质量（单位：千克 kg），a 是加速度（单位：米每二次方秒 m/s²）。在质量不变的情况下，力越大加速度越大；力相同时，质量越大加速度越小。
- m × a. The direction of acceleration is always the same as the direction of the net force.
- 矢量形式：ΣF = m × a，加速度的方向始终与合外力的方向相同。
2. Weight and Gravitational Field Strength | 重量与重力场强度
Weight is the force exerted on a mass due to gravity. It is a crucial concept in structural engineering, vehicle design, and anywhere gravitational loads must be calculated.
重量是重力作用在物体质量上产生的力。在结构工程、车辆设计以及任何需要计算重力荷载的场景中，这都是一个至关重要的概念。
W = m × g
W is weight (N), m is mass (kg), and g is gravitational field strength. On Earth, g is approximately 9.8 N/kg (often rounded to 10 N/kg for GCSE calculations).
W 表示重量（N），m 表示质量（kg），g 是重力场强度。地球表面 g 约为 9.8 N/kg（在 GCSE 计算中常取 10 N/kg）。
Note that weight is a force, so it can cause acceleration according to Newton's Second Law. Mass is a scalar quantity and does not change with location; weight varies with the local gravitational field.
注意重量是一种力，因此依据牛顿第二定律它可以产生加速度。质量是标量，不随位置变化，而重量会随当地重力场变化而变化。
3. Moments and the Principle of Moments | 力矩与力矩平衡原理
A moment is the turning effect of a force about a pivot. This principle is widely used in the design of levers, bridges, and rotating machinery.
力矩是力对某个支点产生的转动效应，广泛应用于杠杆、桥梁和旋转机械的设计中。
M = F × d
Here M is the moment (newton metres, N·m), F is the force (N), and d is the perpendicular distance from the pivot to the line of action of the force (m).
其中 M 为力矩（单位：牛·米 N·m），F 为力（N），d 为支点到力作用线的垂直距离（m）。
nticlockwise moments. This is the Principle of Moments: ΣM(clockwise) = ΣM(anticlockwise).
物体达到转动平衡时，对于任意支点，顺时针力矩之和等于逆时针力矩之和。这就是力矩平衡原理：ΣM(顺时针) = ΣM(逆时针)。
4. Work Done and Energy Transfer | 做功与能量转移
In engineering, work is done when a force moves an object through a distance in the direction of the force. Work is a measure of energy transfer.
在工程中，当一个力使物体沿力的方向移动一段距离时，该力便做了功。功是能量转移的一种量度。
W = F × s
W is work done (joules, J), F is the applied force (N), and s is the displacement in the direction of the force (m). If the force and displacement are not parallel, only the component of force along the displacement is used.
W 表示做功（焦耳 J），F 为施加的力（N），s 为物体在力的方向上移动的距离（m）。若力与位移不平行，则只考虑沿位移方向的分力。
where h is the height gained. This is often used in calculating the energy input required for lifts, cranes, and ramps.
竖直提升物体反抗重力做功为：W = m × g × h，其中 h 是上升高度。此公式常用于计算电梯、起重机和斜坡等所需输入的能量。
5. Kinetic Energy and Gravitational Potential Energy | 动能与重力势能
Energy exists in many forms, but two mechanical forms are central: kinetic energy (due to motion) and gravitational potential energy (due to position in a gravitational field).
能量有多种形式，但两种机械能最为核心：动能（物体因运动而具有的能量）和重力势能（因在重力场中的位置而具有的能量）。
Kinetic energy: KE = ½ × m × v², where m is mass (kg) and v is speed (m/s).
动能：KE = ½ × m × v²，其中 m 为质量（kg），v 为速度（m/s）。
Gravitational potential energy: PE = m × g × h, with g as gravitational field strength (N/kg) and h as height (m).
重力势能：PE = m × g × h，g 为重力场强度 (N/kg)，h 为高度 (m)。
In many engineering problems, such as roller coasters or hydroelectric systems, energy converts between these forms. Ignoring friction, the total mechanical energy (KE + PE) remains constant.
在许多工程问题中，例如过山车或水力发电系统，能量会在这些形式之间转换。忽略摩擦时，总机械能（KE + PE）保持恒定。
6. Power and Efficiency | 功率与效率
Power is the rate at which work is done or energy is transferred. It tells engineers how quickly a machine can perform a task.
功率是做功或能量转移的快慢程度，它告诉工程师一台机器完成任务的速度有多快。
P = W ÷ t
P is power (watts, W), W is work done or energy transferred (J), and t s time (s). For an object moving at constant speed v when a force F is applied: P = F × v.
P 是功率（瓦特 W），W 是做的功或转移的能量（J），t 是时间（s）。当物体在恒力 F 作用下以恒定速度 v 运动时，有 P = F × v。
Efficiency measures how well a device converts input energy into useful output energy. It is never greater than 100% because of energy losses, usually as heat from friction.
效率衡量一个设备将输入能量转化为有用输出能量的能力。由于摩擦等原因造成的能量损失（通常以热的形式），效率永远不会超过 100%。
Efficiency = (Useful output energy ÷ Total input energy) × 100%
或表示成功率：Efficiency = (Useful power output ÷ Total power input) × 100%
7. Ohm's Law and Electrical Power | 欧姆定律与电功率
Ohm’s Law is the fundamental relationship between voltage, current, and resistance in an electrical circuit. It is essential for designing and analysing circuits in all branches of electronic and electrical engineering.
欧姆定律是电路中电压、电流与电阻之间的基本关系，对所有电子与电气工程领域的电路设计和分析都至关重要。
V = I × R
V is potential difference (volts, V), I is current (amperes, A), and R is resistance (ohms, Ω). For a given resistance, current is directly proportional to voltage.
V 表示电势差（伏特 V），I 表示电流（安培 A），R 表示电阻（欧姆 Ω）。对于给定的电阻，电流与电压成正比。
Electrical power is the rate of energy transfer in a circuit. Three useful forms are:
电功率是电路中能量转移的速率，有三个常用的计算公式：
P = I × V
P = I² × R
P = V² ÷ R
These are especially important when choosing components, such as selecting resistors with adequate power ratings to prevent overheating.
这些公式在选择元件时尤其重要，比如选择具有足够功率额定值的电阻以防过热。
8. Resistors in Series and Parallel | 串联与并联电阻
When resistors are combined in a circuit, their total or equivalent resistance can be found using simple rules. This is key for circuit analysis and voltage division.
当电阻在电路中组合时，可通过简单规则求出总电阻或等效电阻。这对电路分析和分压设计至关重要。
Resistors in series: the total resistance is the sum of individual resistances.
串联电阻：总电阻等于各电阻之和。
Rtotal = R₁ + R₂ + R₃ + …
Resistors in parallel: the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.
并联电阻：总电阻的倒数等于各电阻倒数之和。
1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + …
For two resistors in parallel, a shortcut formula is Rtotal = (R₁ × R₂) / (R₁ + R₂). This appears frequently in Edexcel Engineering problems.
对于两个并联电阻，可使用简捷公式：Rtotal = (R₁ × R₂) / (R₁ + R₂)。这在 Edexcel 工程试题中经常出现。
9. Stress, Strain and the Young Modulus | 应力、应变与杨氏模量
When materials are subjected to forces, they undergo deformation. Stress and strain quantify the internal forces and the resulting deformation. These concepts are vital for selecting safe and economical materials in structural engineering.
材料受力时会发生变形。应力和应变用于量化内力和由此产生的变形。这些概念对于结构工程中安全且经济地选材至关重要。
Stress (σ) = F ÷ A
Tensile or compressive stress σ (pascals, Pa or N/m²) is the force F (N) applied over a cross-sectional area A (m²).
拉应力或压应力 σ（帕斯卡 Pa 或 N/m²）等于作用力 F（N）除以横截面积 A（m²）。
Strain (ε) = ΔL ÷ L₀
Strain ε is a dimensionless ratio: the change in length ΔL (m) divided by the original length L₀ (m). It is often expressed as a percentage.
应变 ε 是一个无量纲比值：长度变化 ΔL（m）除以原始长度 L₀（m），常以百分比表示。
Young modulus E describes the stiffness of a material within its elastic limit. It is a property of the material itself.
杨氏模量 E 描述材料在弹性范围内的刚度，是材料本身的属性。
E = stress ÷ strain = σ ÷ ε
10. Hooke's Law and Spring Constant | 胡克定律与弹簧常数
For many elastic materials, the extension is proportional to the applied load up to the limit of proportionality. Hooke's Law governs springs and many load-bearing components.
对于许多弹性材料，在比例极限内，伸长量与所施加的载荷成正比。胡克定律支配着弹簧及许多承重元件的行为。
F = k × x
F is force applied (N), k is spring constant or stiffness (N/m), and x is extension (m). The spring constant indicates how stiff a spring is: a larger k means a stiffer spring.
F 为施加的力（N），k 为弹簧常数或刚度（N/m），x 为伸长量（m）。弹簧常数表示弹簧的刚度：k 值越大，弹簧越硬。
Elastic potential energy stored in a stretched spring can be calculated as:
被拉伸的弹簧中储存的弹性势能可通过下式计算：
E_elastic = ½ × F × x = ½ × k × x²
This energy is important in mechanical systems like vehicle suspensions, shock absorbers, and kinetic energy recovery systems.
此能量在车辆悬架、减震器和动能回收系统等机械系统中非常重要。
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