A solid spherical ball of mass M and radius R rolls without slipping down an inclined plane from a height h.Compare the center of mass speed of the ball at the bottom of the plane with the speed obtained if the ball were simply dropped from a height h. A)rolling ball is (5/7)^1/2 times slower B)rolling ball is 7/5 times faster C)rolling ball is (2/3)^1/2times slower D)rolling ball is 2/3 times faster E)rolling ball and dropped ball have the same speeds

Question

Quizplus · Accepted Answer

When a ball rolls without slipping, its kinetic energy at the bottom is divided between translational and rotational kinetic energy. For a solid sphere, the moment of inertia is (2/5)MR^2, leading to a final speed of the center of mass that is sqrt(5/7) times the speed of a freely falling object. This means the rolling ball is (7/5) times slower, not faster, than if it were simply dropped.

A Solid Spherical Ball of Mass M and Radius R