Loop the Loop
A ball rolls down an inclined track and around a vertical circle. All of the ball's initial potential energy is converted into three forms of energy when it reaches the top of the loop: potential energy corresponding to the height of the loop, kinetic energy corresponding to the ball's velocity, and kinetic energy corresponding to the ball's rotation as it rolls. Knowing that the ball must achieve a certain velocity to make it around the loop and taking all forms of energy into account, one can determine the initial potential energy that the ball must have. This corresponds to an initial height of release.