Two uniform disks, each with the same mass but with radii differing by a factor of 2, roll without slipping down an inclined plane. If the two disks start from rest at the same height h, calculate the ratio of the angular velocity of the small disk divided by that of the larger disk.
A) 1
B) 0.5
C) 4
D) 2
E) 0.25

Question

Quizplus · Accepted Answer

The angular velocity of a rolling disk is given by v/r, where v is the linear velocity and r is the radius. Since the disks start from rest and roll without slipping, they have the same linear velocity at any given time. Therefore, the ratio of the angular velocities is equal to the inverse ratio of the radii, which is 1/2.

Two Uniform Disks, Each with the Same Mass but with Radii