2.4 Uniform circular motion

- An object moving with constant speed along a circular path is said to be in uniform circular motion (UCM).

- Such a motion is only possible if its velocity is always tangential to its circular path, without change in its magnitude.

- To change the direction of velocity, acceleration is a must.

- However, if the acceleration or its component is in line with the velocity (along or opposite to the velocity), it will always change the speed (magnitude of velocity) in which case it will not continue its uniform circular motion.

- In order to achieve both these requirements, the acceleration must be

(i) perpendicular to the tangential velocity,

(ii) of constant magnitude and

(iii) always directed towards the centre of the circular trajectory.

- Such an acceleration is called centripetal (centre seeking) acceleration and the force causing this acceleration is centripetal force.

- Thus, in order to realize a circular motion, there are two requirements;

(i) tangential velocity and

(ii) centripetal force of suitable constant magnitude.

- An example is the motion of the moon going around the Earth in a nearly circular orbit as a result of the constant gravitational attraction of fixed magnitude felt by it towards the Earth.