Why centripetal force doesn't have work?

Centripetal force does not do work because it acts perpendicular to the direction of motion of an object. Work is defined as the force applied to an object in the direction of its motion, causing it to move a certain distance. In the case of centripetal force, the force is always directed towards the center of the circular motion, while the object moves tangentially to the circle. This means that the force does not cause the object to move in the direction of the force, and therefore no work is done.

Centripetal force does have work. Work is defined as the force applied to an object multiplied by the displacement of the object in the direction of the force. In the case of centripetal force, the force is applied perpendicular to the direction of motion, so the displacement is zero. Therefore, the work done by centripetal force is zero.