Edexcel Physics: Mastering Circular Motion – Key Concepts & Exam Tips | Edexcel 物理：圆周运动考点精讲

📚 Edexcel Physics: Mastering Circular Motion – Key Concepts & Exam Tips | Edexcel 物理：圆周运动考点精讲

Circular motion is a core topic in the Edexcel A-level Physics specification (Topic 6: Further Mechanics) and frequently appears in both AS and A2 exam papers. Understanding angular displacement, centripetal acceleration, and the forces that maintain circular paths is essential for tackling problems ranging from conical pendulums to vertical loops. This article distils the key concepts, equations, and common pitfalls, providing a bilingual revision guide to help you master circular motion for Edexcel Physics.

圆周运动是Edexcel A-level物理大纲（Topic 6: Further Mechanics）的核心内容，在AS和A2考试中反复出现。掌握角位移、向心加速度以及维持圆周路径的力，是解答圆锥摆、竖直回环等问题的关键。本文提炼核心概念、公式和常见误区，以中英双语形式帮你攻克Edexcel物理的圆周运动考点。

1. Angular Displacement and Radian Measure | 角位移与弧度制

Angular displacement θ describes the angle through which an object moves along a circular arc. The SI unit is the radian (rad), defined as the angle subtended at the centre of a circle by an arc equal in length to the radius. One complete revolution corresponds to 2π rad, so 1 rad ≈ 57.3°.

角位移θ描述物体沿圆弧转过的角度，SI单位是弧度(rad)。1弧度定义为弧长等于半径的弧所对的圆心角。一整圈对应2π rad，因此1 rad ≈ 57.3°。

Radian measure has no dimensions because it is a ratio of two lengths. Its use is essential in A-level equations; without radians, relationships like v = ωr and a = ω²r would require conversion factors. Always ensure angles are in radians when using these formulas, unless a question specifically instructs otherwise.

弧度制由于是长度比而无量纲。在A-level公式中使用弧度制是必要的；如果不用弧度，v = ωr 和 a = ω²r 等关系将需要引入换算系数。在使用这些公式时，务必确保角度以弧度为单位，除非题目特别说明。

2. Angular Speed, Period and Frequency | 角速度、周期与频率

Angular speed ω is the rate of change of angular displacement. For uniform circular motion, where the object sweeps equal angles in equal times, ω = Δθ / Δt. Since one full rotation is 2π rad and time period T is the time for one revolution, we have ω = 2π / T. Frequency f = 1/T, so also ω = 2π f. The unit of ω is rad s&supmin;¹.

角速度ω是角位移的变化率。对于匀速圆周运动，物体在相等时间内转过相等的角度，ω = Δθ / Δt。由于一整圈为2π rad，周期T为转一圈的时间，故ω = 2π / T。频率f = 1/T，因此也有ω = 2π f。ω的单位为rad s&supmin;¹。

In uniform circular motion, angular speed is constant, but linear speed is constant only in magnitude; the direction changes continuously. This distinction is fundamental when analysing acceleration and force.

在匀速圆周运动中，角速度不变，但线速度仅大小不变，方向不断改变。这一区别在分析加速度和力时非常关键。

3. Relationship Between Linear and Angular Velocity | 线速度与角速度的关系

The linear speed v (tangential speed) is linked to angular speed by v = ωr, where r is the radius of the circle. This can be derived from the arc length s = rθ by differentiating with respect to time: ds/dt = r dθ/dt, giving v = rω.

线速度v（切向速率）与角速度的关系为 v = ωr，r是圆周半径。这可以通过弧长公式 s = rθ 对时间求导得出：ds/dt = r dθ/dt，即 v = rω。

For a rigid, rotating object, all points share the same angular speed ω, but points farther from the axis have a greater linear speed v. This explains why the tip of a fan blade moves faster than points near the hub. In circular motion problems, ensure you use the correct radius for the point under consideration.

对于刚体旋转，所有点角速度ω相同，但离轴越远的点线速度v越大。这解释了风扇叶片尖端比靠近轴心的点移动更快。在圆周运动问题中，务必使用所分析质点的正确半径。

4. Centripetal Acceleration | 向心加速度

Although the magnitude of velocity remains constant in uniform circular motion, the velocity vector changes direction, so there must be an acceleration. This acceleration always points towards the centre of the circle and is called centripetal acceleration. Its magnitude is given by:

a = v² / r = ω² r

虽然匀速圆周运动中速度大小不变，但速度方向改变，因此必定存在加速度。该加速度始终指向圆心，称为向心加速度。其大小为：a = v² / r = ω² r。

The direction can be justified by considering that

Published by TutorHao | Physics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）