Uniform Circular Motion

An object moving with constant speed along a circular path is said to be performing uniform circular motion (UCM). For this to happen, the velocity must remain tangential to the circular path at every instant, without ever changing its magnitude.

Since the direction of the velocity is continuously changing (even though its magnitude is not), some acceleration must be present — a change in direction always requires acceleration, by definition. But that acceleration cannot have any component along the velocity, because any such component would change the object's speed and destroy the "uniform" part of uniform circular motion. So the acceleration responsible for UCM must satisfy three conditions simultaneously: (i) it must be perpendicular to the tangential velocity at every instant, (ii) it must have constant magnitude, and (iii) it must always point toward the centre of the circular path. An acceleration meeting all three conditions is called centripetal ("centre-seeking") acceleration, and the force that produces it is the centripetal force. …