Answer
The angular acceleration is $4.0~rad/s^2$
Work Step by Step
We can express the angular displacement in units of radians:
$\Delta \theta = 8.0~rev \times \frac{2\pi~rad}{1~rev} = 16\pi~rad$
We can find the angular acceleration $\alpha$:
$\Delta \theta = \frac{1}{2}\alpha~t^2$
$\alpha = \frac{2\Delta \theta}{t^2}$
$\alpha = \frac{(2)(16\pi~rad)}{(5.0~s)^2}$
$\alpha = 4.0~rad/s^2$
The angular acceleration is $4.0~rad/s^2$
