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

Question

Quizplus · Accepted Answer

Let the radius of the smaller disc be r and that of the larger disc be 2r. Let the linear acceleration of both discs be a, and let the angular acceleration of the smaller disc be α. Since both discs are rolling without slipping, we have:

a = αr
a = 0.5α(2r)

Solving for α in both equations and equating them, we get:

α = 2a/r
α = a/2r
2a/r = a/2r
r = 2r/4

So the smaller disc will have twice the angular velocity of the larger disc, and the ratio of their angular velocities will be:

2:1 or 2/1 = 2

Therefore, the answer is D) 2.

Two Uniform Discs,each with the Same Mass but with Radii