Introduction To Uniform Circular Motion

Understanding Uniform Circular Motion

Understanding the Laws of Motion

The movement of a body moving in a circle is called circular motion. Now the motion of a body moving in constant speed is called Uniform Circular Motion. In this case, the speed is constant but velocity changes every instant.

uniform circular motion

If a particle is moving in a circle, it must have some acceleration acting towards the centre which is making it move around the centre. Since this acceleration is perpendicular to the velocity of particle at every instant, it is only changing the direction of velocity and not magnitude and that’s why the motion is uniform circular motion. We call this acceleration centripetal acceleration (or radial acceleration), and the force acting towards the centre is called centripetal force.

In case of uniform circular motion, the acceleration is:

ar = v2r = ω2r

If the mass of the particle is m, we can say from second law of motion that:

F = ma

mv2r= mω2r

This is not a special force, actually force like tension or friction may be a cause of origination of centripetal force. When the vehicles turn on the roads, it is the frictional force between tyres and ground which provides the required centripetal force for turning.

So if a particle is moving in uniform circular motion:

1) Its speed is constant

2) Velocity is changing at every instant

3) There is no tangential acceleration

4) Radial (centripetal) acceleration = ω2r

5) v=ωr

In case of non-uniform circular motion, there is some tangential acceleration due to which the speed of particle increases or decreases. The resultant acceleration is the vector sum of radial acceleration and tangential acceleration.

Practise This Question

The magnitude of the centripetal force acting on a body of mass m executing uniform motion in a circle of radius r with speed v is