Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A.The ratio of the magnitude of the radial acceleration of a point on the rim of B to the magnitude of the radial acceleration of a point on the rim of A is:
A)1
B)2
C)1/2
D)4
E)1/4

Question

Quizplus · Accepted Answer

The radial (centripetal) acceleration $a_r$ is given by $a_r = \omega^2 r$, where $\omega$ is the angular speed and $r$ is the radius of the wheel. Since both wheels are identical, their radii are the same. If wheel B spins with twice the angular speed of wheel A ($\omega_B = 2\omega_A$), then the radial acceleration of B is $a_{rB} = (2\omega_A)^2 r = 4\omega_A^2 r$, which is 4 times the radial acceleration of A ($a_{rA} = \omega_A^2 r$). Therefore, the ratio is 4:1.

Two Wheels Are Identical but Wheel B Is Spinning with Twice