📚 AS Cambridge Engineering: Core Knowledge Review | AS剑桥工程：核心知识点梳理
This guide provides a clear and structured review of the fundamental concepts covered in the Cambridge International AS Level Engineering syllabus. From statics and materials to electronics and thermodynamics, mastering these core topics will help you build strong problem-solving skills and exam confidence.
本指南对剑桥国际AS Level工程课程中的基础概念提供了清晰、结构化的梳理。从静力学、材料到电子学和热力学，掌握这些核心主题将帮助你培养扎实的问题解决能力和考试信心。
1. Introduction to Engineering and Units | 工程概论与单位
Engineering relies on precise measurement and standard units. In the Cambridge AS course, you will use the SI system (Système International), which includes base units such as metre (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, and kelvin (K) for temperature. All derived units, like the newton (N) for force or the pascal (Pa) for pressure, are built from these bases.
工程学依赖于精确的测量和标准单位。在剑桥AS课程中，你将使用国际单位制（SI），基本单位包括米 (m) 表示长度、千克 (kg) 表示质量、秒 (s) 表示时间、安培 (A) 表示电流、开尔文 (K) 表示温度。所有导出单位，如力的牛顿 (N) 或压力的帕斯卡 (Pa)，均由这些基本单位构建而成。
Engineers frequently convert between multiples, such as kilo (10³), mega (10⁶) and milli (10⁻³). Dimensional analysis can be used to check the consistency of equations, ensuring that both sides of a formula have the same base dimensions.
工程师经常在倍数单位之间转换，例如千 (10³)、兆 (10⁶) 和毫 (10⁻³)。量纲分析可用于检验方程的一致性，确保公式两侧具有相同的基本量纲。
2. Forces and Free-Body Diagrams | 力与受力图
A force is a vector quantity that can cause an object to accelerate or deform. Common forces encountered in engineering include weight (W = mg), normal reaction, tension, friction, and applied loads. A free-body diagram (FBD) isolates a single body and shows all the external forces acting on it with labelled arrows.
力是可以使物体加速或变形的矢量。工程中常见的力包括重力 (W = mg)、法向反力、张力、摩擦力和施加的载荷。受力图 (FBD) 将单个物体隔离，并用带标注的箭头显示所有作用在其上的外力。
When drawing an FBD, always place the force arrows at the point of application and choose a coordinate system. Resolving a force into perpendicular components is an essential skill: for a force F at angle θ, the horizontal component is F cos θ and the vertical component is F sin θ.
绘制受力图时，务必将力的箭头放在作用点，并选定坐标系。将力分解为垂直分量是一项基本技能：对于与水平成 θ 角的力 F，水平分量为 F cos θ，垂直分量为 F sin θ。
Fx = F cos θ, Fy = F sin θ
Fₓ = F cos θ， Fy = F sin θ
3. Statics and Equilibrium | 静力学与平衡
A body is in static equilibrium when it remains at rest. For this to occur in two dimensions, the net force in any direction must be zero and the sum of moments about any point must also be zero. These conditions are written as: ΣFx = 0, ΣFy = 0, and ΣM = 0.
当物体保持静止时，它就处于静力平衡。在二维条件下，要实现平衡，任意方向上的净力必须为零，同时绕任意点的合力矩也必须为零。这些条件可写作：ΣFx = 0，ΣFy = 0，以及 ΣM = 0。
Using these equations, you can solve for unknown forces in structures such as trusses, simply supported beams, and frames. It is crucial to assume a consistent sign convention, for instance taking upward forces and counter‑clockwise moments as positive.
利用这些方程，你可以求解桁架、简支梁和框架等结构中的未知力。采用一致的符号约定至关重要，例如规定向上的力和逆时针力矩为正。
4. Moments and Torque | 力矩与扭矩
The moment of a force about a point is a measure of its turning effect. It is calculated as the product of the force and the perpendicular distance from the point to the line of action of the force.
力对某点的力矩是衡量其转动效应的量。它等于力与从该点到力作用线的垂直距离的乘积。
M = F × d
M = F × d
The principle of moments states that for a system in equilibrium, the sum of clockwise moments equals the sum of counter‑clockwise moments. This principle is applied when analysing levers, pulley systems, and beam reactions. Torque is the term used when a moment causes rotation in shafts and rotating machinery.
力矩原理指出，对于处于平衡的系统，顺时针力矩之和等于逆时针力矩之和。在分析杠杆、滑轮系统和梁的支座反力时，会应用这一原理。当力矩导致轴和旋转机械产生转动时，就称为扭矩。
5. Kinematics | 运动学
Kinematics describes the motion of objects without considering the forces involved. The key quantities are displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). For uniformly accelerated motion in a straight line, four fundamental equations apply.
运动学描述物体的运动，而不考虑所涉及的力。关键量包括位移 (s)、初速度 (u)、末速度 (v)、加速度 (a) 和时间 (t)。对于直线上的匀加速运动，有四个基本方程适用。
v = u + a t s = u t + ½ a t² v² = u² + 2 a s s = ½ (u + v) t
v = u + a t s = u t + ½ a t² v² = u² + 2 a s s = ½ (u + v) t
When motion involves projectiles, the horizontal and vertical components are treated independently. Horizontal velocity remains constant (neglecting air resistance), while vertical motion is influenced by gravitational acceleration g (≈ 9.81 m/s²).
当涉及抛体运动时，水平和垂直分量需要独立处理。水平速度保持不变（忽略空气阻力），而垂直运动受重力加速度 g (≈ 9.81 m/s²) 的影响。
6. Dynamics and Newton’s Laws | 动力学与牛顿定律
Dynamics connects forces to motion through Newton’s three laws. The first law states that an object remains at rest or in uniform motion unless acted upon by a net external force. The second law quantifies this relationship: Fnet = m a, where Fnet is the resultant force and m is mass.
动力学通过牛顿三定律将力与运动联系起来。第一定律指出，除非受到净外力作用，否则物体将保持静止或匀速直线运动。第二定律量化了这一关系：Fnet = m a，其中 Fnet 为合力，m 为质量。
The third law asserts that for every action, there is an equal and opposite reaction. This concept is vital for analysing interacting bodies, such as thrust in engines or forces at joints. Friction, often modelled as Ff = μ R, where μ is the coefficient of friction and R is the normal reaction, plays a central role in dynamics problems.
第三定律断言，每一个作用力都有一个大小相等、方向相反的反作用力。这一概念对于分析相互作用的物体（如发动机推力或接头处的力）至关重要。摩擦力通常建模为 Ff = μ R，其中 μ 为摩擦系数，R 为法向反力，在动力学问题中起着核心作用。
7. Energy, Work and Power | 能量、功和功率
Work done by a constant force is the product of the force and the distance moved in the direction of the force: W = F d cos θ. In the SI system, work and energy are measured in joules (J). Energy can exist in many forms, including kinetic energy (KE = ½ m v²) and gravitational potential energy (PE = m g h).
恒力所做的功等于力与沿力方向移动距离的乘积：W = F d cos θ。在国际单位制中，功和能量以焦耳 (J) 为单位。能量可以以多种形式存在，包括动能 (KE = ½ m v²) 和重力势能 (PE = m g h)。
The principle of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another. For mechanical systems where no external work is done, the total mechanical energy (KE + PE) remains constant. Power is the rate of doing work, P = W / t, and is measured in watts (W).
能量守恒定律指出，能量不能被创造或消灭，只能从一种形式转换为另一种形式。对于没有外力做功的机械系统，总机械能 (KE + PE) 保持恒定。功率是做功的速率，P = W / t，单位为瓦特 (W)。
8. Fluid Mechanics | 流体力学
Fluid mechanics deals with liquids and gases at rest or in motion. Pressure in a static fluid increases with depth according to p = ρ g h, where ρ is the fluid density. The pressure at any point in a confined incompressible fluid is transmitted equally in all directions (Pascal’s principle), which is the basis for hydraulic systems.
流体力学研究静止或运动中的液体和气体。静态流体中的压力随深度增加，关系为 p = ρ g h，其中 ρ 为流体密度。在封闭的不可压缩流体中，任一点的压强会向各个方向等值传递（帕斯卡原理），这是液压系统的基础。
When a fluid flows steadily, the continuity equation applies: A₁ v₁ = A₂ v₂, where A is cross‑sectional area and v is flow velocity. Bernoulli’s equation describes energy conservation in a streamline flow: p + ½ ρ v² + ρ g h = constant. These principles are used to analyse pipe flow, nozzles, and aircraft wing lift.
当流体稳定流动时，连续性方程适用：A₁ v₁ = A₂ v₂，其中 A 为横截面积，v 为流速。伯努利方程描述了流线流动中的能量守恒：p + ½ ρ v² + ρ g h = 常数。这些原理被用于分析管道流动、喷嘴和飞机机翼升力。
9. Materials Science and Properties | 材料科学与性能
Selecting the right material is fundamental to engineering design. Key mechanical properties include strength (ability to withstand load without failure), stiffness (resistance to deformation), ductility (ability to be drawn into wire), toughness (energy absorbed before fracture), and hardness (resistance to indentation).
选择合适的材料是工程设计的基础。关键力学性能包括强度（承受载荷而不失效的能力）、刚度（抵抗变形的能力）、延展性（可被拉成丝的能力）、韧性（断裂前吸收的能量）和硬度（抵抗压入的能力）。
| Material | Density (kg/m³) | Tensile Strength (MPa) | Young’s Modulus (GPa) |
|---|---|---|---|
| Mild steel | 7850 | 400 – 550 | 210 |
| Aluminium alloy | 2700 | 200 – 300 | 70 |
| Polycarbonate | 1200 | 60 – 70 | 2.3 |
Stress (σ) is defined as force per unit area, σ = F / A. Strain (ε) is the extension per unit length, ε = ΔL / L₀. Hooke’s law states that stress is proportional to strain within the elastic limit: σ = E ε, where E is Young’s modulus. Beyond the yield point, permanent plastic deformation occurs.
应力 (σ) 定义为每单位面积上的力，σ = F / A。应变 (ε) 是每单位长度的伸长量，ε = ΔL / L₀。胡克定律指出，在弹性极限内，应力与应变成正比：σ = E ε，其中 E 是杨氏模量。超过屈服点后，将发生永久塑性变形。
10. Electronics and Circuit Theory | 电子学与电路理论
Basic circuit analysis requires a solid understanding of Ohm’s law: V = I R, where V is voltage, I is current, and R is resistance. Resistors in series combine as Rtotal = R₁ + R₂ + … , while resistors in parallel follow 1/Rtotal = 1/R₁ + 1/R₂ + … .
基本电路分析需要扎实理解欧姆定律：V = I R，其中 V 为电压，I 为电流，R 为电阻。串联电阻的总电阻为 Rtotal = R₁ + R₂ + …，而并联电阻遵循 1/Rtotal = 1/R₁ + 1/R₂ + …。
Kirchhoff’s rules are essential for more complex networks: the current law (KCL) states that the sum of currents entering a junction equals the sum leaving, while the voltage law (KVL) states that the sum of electromotive forces and potential differences around any closed loop is zero.
基尔霍夫定律对于更复杂的电路网络至关重要：电流定律 (KCL) 指出，流入节点的电流之和等于流出电流之和；电压定律 (KVL) 指出，沿任意闭合回路，电动势和电势差的代数和为零。
Power in an electrical circuit is given by P = V I. Components such as diodes, LEDs, and transistors are also introduced in the AS course, along with sensing circuits using thermistors and light‑dependent resistors (LDRs).
电路中的功率由 P = V I 给出。AS 课程还会介绍二极管、LED 和晶体管等元件，以及使用热敏电阻和光敏电阻 (LDR) 的传感电路。
11. Thermodynamics | 热力学
Thermodynamics studies the relationships between heat, work and energy. The first law of thermodynamics is a statement of energy conservation: ΔU = Q – W, where ΔU is the change in internal energy, Q is heat added to the system, and W is work done by the system.
热力学研究热、功和能量之间的关系。热力学第一定律是能量守恒的表述：ΔU = Q – W，其中 ΔU 是内能的变化量，Q 是系统吸收的热量，W 是系统对外做的功。
Heat transfer occurs in three modes: conduction, convection and radiation. Conduction through a solid bar is described by Fourier’s law: Q̇ = -k A (dT/dx). In many engineering applications, the overall heat transfer coefficient and thermal resistance concepts are used to design heat exchangers and insulators.
热量传递以三种方式进行：热传导、对流和热辐射。通过固体杆的导热由傅里叶定律描述：Q̇ = -k A (dT/dx)。在许多工程应用中，会使用总传热系数和热阻的概念来设计换热器和保温层。
The gas laws, including Boyle’s law (p V = constant at constant T) and Charles’s law (V / T = constant at constant p), lead to the ideal gas equation: p V = n R T, where R = 8.31 J/(mol·K). This equation is central to thermodynamic cycles, such as the Otto and Diesel cycles studied in internal combustion engines.
气体定律，包括玻意耳定律（在 T 恒定时 p V = 常数）和查理定律（在 p 恒定时 V / T = 常数），最终引出理想气体状态方程：p V = n R T，其中 R = 8.31 J/(mol·K)。该方程是热力学循环（如内燃机中研究的奥托循环和狄塞尔循环）的核心。
12. Engineering Drawing and Communication | 工程制图与沟通
Engineering drawings are the universal language of design. Orthographic projection uses multiple 2D views (front, top, side) to represent a 3D object in accordance with British Standard BS 8888. Dimensioning must be clear, with all linear distances, radii, and angles unambiguously shown.
工程图纸是设计的通用语言。正投影根据英国标准 BS 8888，使用多个二维视图（前视图、俯视图、侧视图）来表达三维物体。尺寸标注必须清晰，所有线性距离、半径和角度都应明确标注。
Other drawing conventions include isometric projection, section views, and exploded diagrams. Symbols for welding, surface finish, and tolerances are also introduced. Being able to interpret and create these drawings accurately is an essential skill assessed in the examination, often through sketching or CAD‑style questions.
其他绘图规范包括等轴测投影、剖视图和爆炸图。还会介绍焊接符号、表面粗糙度和公差。能够准确解读和绘制这些图纸是考试中评估的基本技能，通常通过草图或CAD风格的问题进行考查。
Effective communication in engineering also requires understanding standard components, fasteners, and material specifications, making the link between the design office and the workshop seamless.
工程中的有效沟通还需要了解标准件、紧固件和材料规格，从而实现设计室和车间之间的无缝衔接。
Published by TutorHao | Engineering Revision Series | aleveler.com
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