For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on the rim to the radial acceleration of a point halfway between the center and the rim is:
A)1
B)2
C)1/2
D)4
E)1/4

Question

Quizplus · Accepted Answer

The radial acceleration of a point on the rim is a = v^2/r, where v is the tangential velocity and r is the radius. The tangential velocity is proportional to the distance from the axis, so v_rim = r*w, and v_center = (r/2)*w. Therefore, the ratio of the radial acceleration at the rim to the radial acceleration at the center is (v_rim)^2/(v_center)^2 = (r*w)^2/[(r/2)*w]^2 = 4, which means that the answer is choice B.

For a Wheel Spinning on an Axis Through Its Center