Answer
(a) $v = R\sqrt{2\alpha \Delta \theta}$
(b) $a_c = R(2\alpha \Delta \theta) $
Work Step by Step
(a) We can find the angular velocity after the wheel rotates through an angle of $\Delta \theta$;
$\omega^2 = \omega_0^2+2\alpha \Delta \theta$
$\omega^2 = 0+2\alpha \Delta \theta$
$\omega = \sqrt{2\alpha \Delta \theta}$
We can find the velocity;
$v = \omega ~R = R\sqrt{2\alpha \Delta \theta}$
(b) We can find the centripetal acceleration;
$a_c = \omega^2 ~R$
$a_c = (\sqrt{2\alpha \Delta \theta})^2 ~R$
$a_c = R(2\alpha \Delta \theta) $
