Answer
The angular acceleration is $0.39~rad/s^2$
Work Step by Step
We can express the angular speed in units of $rad/s$:
$\omega = 0.50~rev/s \times \frac{2\pi~rad}{1~rev} = \pi~rad/s$
We can express the angular displacement in units of radians:
$\Delta \theta = 2.0~rev \times \frac{2\pi~rad}{1~rev} = 4\pi~rad$
We can find the angular acceleration $\alpha$:
$\omega_f^2 = \omega_0^2+2\alpha~\Delta \theta$
$\alpha = \frac{\omega_f^2 - \omega_0^2}{2~\Delta \theta}$
$\alpha = \frac{(\pi~rad/s)^2 - 0}{(2)(4\pi~rad)}$
$\alpha = 0.39~rad/s^2$
The angular acceleration is $0.39~rad/s^2$
