A level Physics · Edexcel 9PH0 · Topic 6B

Circular motion

Key points

Angular displacement is measured in radians: $\theta = \frac{s}{r}$ , and $2\pi$ rad = 360°.
Angular velocity $\omega = \frac{\Delta\theta}{\Delta t} = \frac{2\pi}{T} = 2\pi f$ ; linear speed $v = \omega r$ .
An object moving at constant speed in a circle has a changing velocity, so it accelerates towards the centre: $a = \frac{v^2}{r} = r\omega^2$ .
Centripetal force is the resultant force towards the centre: $F = \frac{mv^2}{r} = mr\omega^2$ . It is not an extra force; it is provided by tension, friction, gravity, etc.
On a loop or vertical circle, at the top weight and the normal force both point to the centre; at the bottom the normal force must exceed the weight.
If the centripetal force is removed, the object moves off along a tangent.
Exam tip: draw a free-body diagram, find the resultant towards the centre and set it equal to $\frac{mv^2}{r}$ .

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An object moving in a circle at constant speed is still accelerating, because its direction keeps changing. These notes cover radians, angular velocity, centripetal acceleration and force, and how to analyse real circular motion.

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