Answer
(a) $\omega_1 = \omega_2 =\omega_3$
(b) $v_3 > v_1 = v_2$
Work Step by Step
(a) $\omega_1 = \omega_2 =\omega_3$
Each point on the wheel rotates through the same angle per unit time.
(b) $v_3 > v_1 = v_2$
For a point on a rotating wheel, $v = \omega ~r$, where $r$ is the distance from the axis of rotation. Since point 3 is farthest from the center, point 3 moves a larger distance than point 1 and point 2 per unit time. Therefore, the speed of point 3 is greater than the speed of point 1 and point 2.
Note that point 1 and point 2 move at the same speed since they are the same distance from the center.
