Consider a ball of mass m that is tied to a string of length r and is being whirled at constant speed in a horizontal circular path over a smooth horizontal table as shown in Figure 23 (a). Its weight is supported by a frictionless table. Why does the ball move in a circle?

According to Newton’s first law, the ball tends to move in a straight line; however, the string prevents motion along a straight line by exerting on the ball a radial force F_c that makes it follow the circular path. This force is directed along the string toward the center of the circle, and it is known as centripetal (radial) force. If we apply Newton’s second law along the radial direction, we find that the net force causing the centripetal acceleration, i.e., the centripetal force, is expressed as