# Centripetal force

If a body moves in a circle there must be a resultant force acting towards the centre. This is because the change in direction implies that the body is accelerating.

Deriving the equation is not so simple though...

Key Concepts

Perpendicular force

A force acting at right angles to the direction of motion causes the body to travel in a circular path.

Relationship between ω and v

ω is the angular velocity = $$2\pi \over T$$
v is the speed = $$2\pi r \over T$$

From this we can deduce that $$v = ωr$$

Essentials

When deriving the equation for centripetal acceleration we start by considering a small part of the motion we can deduce that

$$a = {mv^2\over r}$$

This is the acceleration.

Test Yourself

Use quizzes to practise application of theory.

Exam-style Questions