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LearnCambridge9231Current syllabusPaper 3 · Further MechanicsCircular motion

Paper 3 · Module

Circular motion

2 subtopics≈ 70 min in total

Start the module: Kinematics of circular motion Open graphing calculator

Kinematics of circular motion
Angles in circular motion are measured in radians: $\theta=\dfrac sr$ , so a full turn is $2\pi$ rad. Angular speed $\omega$ is the rate of change of angle, $\omega=\dfrac{2\pi}T=2\pi f$ . A point at radius $r$ moves with linear speed $v=r\omega$ . Every point on a rigid rotating object has the same $\omega$ , but points further out move faster.
≈ 30 min
Centripetal acceleration and force
An object moving in a circle accelerates towards the centre: $a=\dfrac{v^2}r=r\omega^2$ . This needs a resultant force towards the centre, $F=\dfrac{mv^2}r=mr\omega^2$ , called the centripetal force. It isn't a new kind of force: tension, gravity, friction or a normal reaction provides it. Being perpendicular to the velocity, it changes direction but does no work.
≈ 40 min