Chapter 6, Problem 1CQ

If there is a net force on a particle in uniform circular motion, why doesn’t the particle’s speed change?

To determine

The reason for which the speed of a particle in uniform circular motion doesn’t change even though there is a net force on it.

Answer to Problem 1CQ

There is no component of acceleration in the direction tangential to the circular path along which the instantaneous velocity points So the speed of the particle in uniform circular motion doesn’t change even though there is a net force on it.

Explanation of Solution

In uniform circular motion the particle moves in a circular path such that the centripetal force acting on the particle. The centripetal force is acting towards the center of the circular path. As per the Newton’s second law, the particle possesses a radial acceleration corresponding to the centripetal force and it is called centripetal acceleration. The direction of the instantaneous velocity of the particle is directed along the tangent of the circular path in each instant. Thus, the direction of velocity of the particle changes in each instant.

The centripetal acceleration is also directed towards the center of the circular path. There is no component of this centripetal acceleration in the direction of the instantaneous velocity which is the tangential direction of the circular path. Thus, there is no increase in the magnitude of the instantaneous velocity, which is the speed of the particle remains same at each instant.