## Illustration 6.5: Circular Motion

set v and play: no external force | set v and play: gravity

Please wait for the animation to completely load.

A 1-kg black ball is constrained to move in a circle as shown in the animation **(position is given in meters, time is given in seconds, and energy on the bar graph is given in joules)**. Restart. In the no external force animation the wire is horizontal on a frictionless tabletop and the force of the wire is the only force that acts. In the gravity animation the wire is vertical and the ball is subjected to gravity (downward as usual) as well as the force of the wire. You may set the initial velocity and then choose either configuration. The blue arrow represents the net force acting on the mass, while the bar graph displays its kinetic energy in Joules.

For no external force, select various initial velocities and then set v and play: no external force. In what direction does the net force point? Here the only force acting is the force of the wire pulling on the ball to make it go in a circle. The direction of this force is always toward the center of the circle (a centripetal force). With this force, does the black ball's speed change? No. The ball's velocity changes, but its speed does not. The work-energy theorem tells us that since there is no work done by the force of the wire (its force is perpendicular to the ball's displacement) there can be no change in the ball's kinetic energy. In general, any centripetal force cannot ever do work.

For gravity, select various initial velocities and then set v and play: gravity. In what direction does the net force point now? Well, this is a bit more complicated. There is a force toward the center of the circle as there was before (again due to the wire), but now there is also the force of gravity downward. Therefore, the net force does not point toward the center of the circle any more. With this force, does the black ball's speed change? Yes. While the part of the force due to the wire cannot do any work, the part of the force that is due to gravity can and does do work.