📚 Edexcel M1 Book: Core Mechanics Topics | Edexcel M1 教材：力学核心主题
This revision guide covers the essential content of the Edexcel Mechanics 1 (M1) textbook. It focuses on the modelling assumptions, kinematics, dynamics, statics, momentum and moments skills that are regularly tested. Use this article alongside your M1 textbook and past papers to build confidence.
本篇复习指南涵盖 Edexcel Mechanics 1（M1）教材的核心内容。文章重点讲解考试中经常考查的建模假设、运动学、动力学、静力学、动量与力矩技能。建议结合 M1 教材和历年真题一起使用，以增强应试信心。
1. Mathematical Modelling in M1 | M1 中的数学建模
In Edexcel Mechanics 1, you are expected to build a simplified mathematical model from a real-world situation. The exam often asks you to state modelling assumptions and explain why they make the problem easier to solve. Common assumptions include treating a car as a particle, a string as light and inextensible, a pulley as smooth, and air resistance as negligible.
在 Edexcel Mechanics 1 中，你需要从现实情境中建立简化的数学模型。考试经常要求你陈述建模假设，并解释为什么这些假设可以使问题更容易求解。常见的假设包括：将汽车视为质点、将绳子视为轻且不可伸长、将滑轮视为光滑、将空气阻力忽略不计。
Modelling assumptions affect validity. For example, treating a car as a particle ignores its length and rotation, which is only valid if its dimensions are small compared with the distances travelled.
建模假设会影响模型的有效性。例如，将汽车视为质点就忽略了它的长度和转动，只有在其尺寸远小于运动距离时才是合理的。
- Particle: mass concentrated at a point, no rotation | 质点：质量集中在一个点，无转动。
- Light string: zero mass, tension constant along the string | 轻绳：质量为零，沿绳张力不变。
- Inextensible string: connected bodies have the same acceleration | 不可伸长绳：相连物体加速度相同。
- Smooth pulley: no friction, tension is the same on both sides | 光滑滑轮：无摩擦，两侧张力相同。
- Rigid body: distances between particles remain fixed | 刚体：各点之间距离保持不变。
2. Scalars and Vectors | 标量与矢量
Scalars have magnitude only, while vectors have both magnitude and direction. In M1, speed and distance are scalars; displacement, velocity, acceleration and force are vectors. You must be confident in adding vectors, resolving them into components, and finding their magnitude and direction.
标量只有大小，而矢量既有大小又有方向。在 M1 中，速率和路程是标量；位移、速度、加速度和力是矢量。你必须熟练掌握矢量的加法、分解以及求大小和方向。
Example: A force F = 3i + 4j N has magnitude |F| = √3² + 4² = 5 N and direction θ = tan⁻¹(4/3) ≈ 53.1° from the positive i direction.
示例：一个力 F = 3i + 4j N 的大小为 |F| = √3² + 4² = 5 N，方向为 θ = tan⁻¹(4/3) ≈ 53.1°，从正 i 方向量起。
j components separately. For a force F₁ = a i + b j and F₂ = c i + d j, the resultant is F
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