A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane.If both are uniform,which one reaches the bottom of the incline first if there is no slipping?
A)the hoop
B)the disk
C)Both reach the bottom at the same time.

Question

Quizplus · Accepted Answer

Both the disk and the hoop will have the same gravitational potential energy at the top of the incline. As there is no slipping, both will reach the bottom of the incline with the same kinetic energy. However, the moment of inertia of a hoop is greater than that of a disk (I_hoop = MR^2 and I_disk = (1/2)(MR^2)), which means that the hoop has a greater resistance to rotational motion (i.e., harder to start and stop rotating). Therefore, the hoop will take longer to roll down the incline compared to the disk, which will reach the bottom first.

A Disk and a Hoop of the Same Mass and Radius