Answer
(a) $\omega = 98~rpm$
(b) The wheel makes 12 revolutions during this time.
Work Step by Step
We can find the change in angular velocity.
$\Delta \omega = \alpha ~t$
$\Delta \omega = (0.50~rad/s^2)(10~s)$
$\Delta \omega = 5.0~rad/s$
We can convert this to units of rpm.
$\Delta \omega = (5.0~rad/s)(\frac{1~rev}{2\pi~rad})(\frac{60~s}{1~min})$
$\Delta \omega = 48~rpm$
We can find the angular velocity after 10 seconds.
$\omega = \omega_0+\Delta \omega$
$\omega = 50~rpm+48~rpm$
$\omega = 98~rpm$
(b) We can find the number of revolutions that the wheel rotates through in this time.
$\theta = (\frac{\omega_0+\omega_f}{2})(10~s)$
$\theta = (\frac{50~rpm+98~rpm}{2})(\frac{1}{6}~min)$
$\theta = 12~rev$
The wheel makes 12 revolutions during this time.
