IGCSE AQA Physics: Circular Motion Key Points | IGCSE AQA 物理：圆周运动考点精讲

📚 IGCSE AQA Physics: Circular Motion Key Points | IGCSE AQA 物理：圆周运动考点精讲

Circular motion is a fundamental concept in IGCSE AQA Physics. It describes the movement of an object along a circular path at constant speed. Even though the speed may not change, the direction of the velocity is continuously changing, which means the object is accelerating. This acceleration is directed towards the centre of the circle and requires a net inward force called the centripetal force. In this article, we will cover the essential ideas, equations, and examples you need for your exam.

圆周运动是IGCSE AQA物理中的一个基本概念。它描述了一个物体沿圆形路径以恒定速率运动。尽管速率可能不变，但速度的方向不断变化，这意味着物体在加速。这种加速度指向圆心，需要一个指向圆心的合力，即向心力。在本文中，我们将涵盖考试所需的基本概念、方程和实例。

1. What is Circular Motion? | 什么是圆周运动？

An object in circular motion travels in a circle. The distance from the centre remains constant. Common examples include a car going around a roundabout, a planet orbiting the Sun, or an electron orbiting the nucleus (though that is quantum, we simplify in classical physics). In uniform circular motion, the speed of the object is constant, but its velocity changes because the direction of motion changes at every point.

做圆周运动的物体沿圆形路径运动。它到圆心的距离保持不变。常见的例子包括汽车绕环岛行驶、行星绕太阳运行，或电子绕原子核运动（尽管是量子现象，但在经典物理中我们简化处理）。在匀速圆周运动中，物体的速率不变，但由于运动方向在每一点都变化，速度也不断变化。

The velocity vector is always tangent to the circle at the object’s position. Thus, the object is never moving towards or away from the centre; it moves perpendicular to the radius.

速度矢量始终与物体所在位置的圆相切。因此，物体从不朝向或远离圆心运动；它垂直于半径运动。

In uniform circular motion, the magnitude of the acceleration is constant, but its direction changes continuously, always towards the centre. This acceleration is responsible for changing only the direction of velocity, not its magnitude.

在匀速圆周运动中，加速度的大小恒定，但方向不断变化，始终指向中心。这个加速度只改变速度的方向，而不改变其大小。

2. Speed and Velocity: Direction Matters | 速率与速度：方向至关重要

In linear motion, speed and velocity are often used interchangeably, but in circular motion the distinction is crucial. Speed is the magnitude of how fast an object moves: v = distance / time. For one complete circle, distance is the circumference, 2πr. Velocity is speed in a given direction. Since the direction changes, velocity is not constant even if speed is.

在直线运动中，速率和速度常常可以互换使用，但在圆周运动中，区分它们至关重要。速率是物体移动快慢的量度：v = 距离 / 时间。对于一整圈，距离是圆周长2πr。速度是给定方向上的速率。由于方向变化，即使速率恒定，速度也不恒定。

This changing velocity means there is an acceleration. According to Newton’s first law, a force must be acting to cause this acceleration. The instantaneous velocity vector is always at a tangent to the circle, while the centripetal acceleration vector points radially inward. These two vectors are perpendicular at every instant.

这种速度的变化意味着存在加速度。根据牛顿第一定律，必须有作用力来导致这种加速度。瞬时速度矢量始终与圆相切，而向心加速度矢量则沿径向指向圆心。这两个矢量在每一瞬时都互相垂直。

3. Angular Velocity and Linear Speed | 角速度与线速度

Angular velocity (ω) is a measure of how quickly an object rotates. It is the angle an object sweeps out per unit time, usually measured in radians per second (rad/s). For one full revolution, the angle is 2π radians. One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius, which makes it a dimensionless ratio, but we use the label rad to clarify.

角速度（ω）是衡量物体转动快慢的物理量。它是物体在单位时间内扫过的角度，通常以弧度每秒（rad/s）为单位。一整圈的角度为2π弧度。一个弧度是指弧长等于半径时所对的圆心角，这使得弧度成为无量纲的比值，但我们使用rad作标记以示区分。

The linear speed v is related to angular velocity by the equation:

线速度v与角速度的关系由以下方程给出：

v = ω r

where r is the radius of the circle. This formula is fundamental for converting between angular and linear quantities. If an object moves faster or if the radius is larger, the linear speed increases for a given angular velocity.

其中r是圆的半径。这个公式是角量和线量相互转换的基础。对于给定的角速度，如果物体运动更快或半径更大，线速度就增大。

4. The Period and Frequency of Circular Motion | 圆周运动的周期与频率

The period (T) is the time taken for one complete revolution. It is measured in seconds (s). Frequency (f) is the number of revolutions per second, measured in hertz (Hz). They are inversely related:

周期（T）是完成一整圈所需的时间，单位为秒（s）。频率（f）是每秒转的圈数，单位为赫兹（Hz）。它们互为倒数：

f = 1 / T and T = 1 / f

Since the object travels a distance of 2πr in time T, the speed can also be written as:

由于物体在时间T内运动了2πr的距离，速率也可写为：

v = 2πr / T

And angular velocity is:

而角速度为：

ω = 2π / T or ω = 2π f

You can combine these to check v = ωr. These relations are particularly useful when you need to find speed or acceleration from timing experiments.

你可以将这些公式结合起来验证v = ωr。当你需要通过计时实验求速度或加速度时，这些关系式特别有用。

5. Understanding Centripetal Acceleration | 理解向心加速度

Any object moving in a circle experiences an acceleration towards the centre. This centripetal acceleration changes the direction of the velocity without changing its magnitude (in uniform circular motion). The magnitude of centripetal acceleration is given by:

任何做圆周运动的物体都经历指向圆心的加速度。这种向心加速度改变速度的方向而不改变其大小（在匀速圆周运动中）。向心加速度的大小由下式给出：

a = v² / r

or, using ω:

或者使用ω：

a = ω² r

Notice that acceleration depends on the square of the speed or angular velocity. Doubling the speed increases the acceleration by a factor of four for the same radius. Using a vector diagram, the change in velocity Δv over a short time interval points towards the centre, proving the direction of acceleration.

注意加速度取决于速度的平方或角速度的平方。对于相同的半径，速度加倍会使加速度增大为原来的四倍。借助矢量图，短时间内速度变化Δv指向中心，证明了加速度的方向。

6. Centripetal Force: The Net Force Towards the Centre | 向心力：指向圆心的合力

According to Newton’s second law, a resultant force is needed to produce an acceleration. For circular motion, this is the centripetal force, directed towards the centre of the circle. The equation is:

根据牛顿第二定律，需要一个合力来产生加速度。对于圆周运动，这个力就是向心力，指向圆心。方程为：

F = m v² / r

F = m ω² r

where m is the mass of the object.

其中m是物体的质量。

Centripetal force is not a new type of force; it is the name given to the resultant force acting towards the centre. It could be tension, friction, gravity, or a combination of forces. Never draw ‘centripetal force’ as an extra arrow on a free-body diagram – instead, label the real forces and show that their vector sum points inward.

向心力不是一种新的

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IGCSE AQA Physics: Circular Motion Key Points | IGCSE AQA 物理：圆周运动 考点精讲