Answer
Time taken to rotate through first 2 rev $= 4$ $seconds$
Work Step by Step
The angular acceleration is constant, so we can use the rotation equations.
Here we can use the equation,
$\theta-\theta_{o}= \omega_{o}t+\frac{1}{2}\alpha t^{2}$
because the only unknown variable is the desired time $t$.
For consistency of units, $\theta-\theta_{o}=2$ $rev$ can be written as $2\times 2\pi$ $rad = 4\pi$ $rad$ as $1$ $rev=2 \pi$ $rad$.
Substituting the known values and setting $\omega_{o}=0$ and $\alpha= 1.50$ $rad/s^{2}$ in the equation and solving gives us,
$4\pi=(0)t+\frac{1}{2}(1.50)t^{2}$
$8\pi/1.50=t^{2}$
$t=\sqrt {16.7}$
$t\approx 4.0$ $s$
