Answer
8.5 revolutions
Work Step by Step
(a) We know that the CD speeds up with uniform velocity. First, we determine the angular acceleration so that we can we ultimately calculate the angular displacement or number of revolutions.
(b) We know that
$\alpha=\frac{\omega-\omega_{\circ}}{t}$
We plug in the known values to obtain:
$\alpha=\frac{\frac{310}{60}rev/s-0rev/s}{3.3s}$
$\alpha=1.56rev/s^2$
Now the angular displacement is given as
$\theta-\theta_{\circ}=(\frac{\omega^2-\omega_{\circ}^2}{2\alpha})$
We plug in the known values to obtain:
$\theta-\theta_{\circ}=\frac{1}{2(1.56rev/s^2)}[(\frac{310}{60}rev/s)^2-(0rev/s)]$
$\implies \theta-\theta_{\circ}=8.5rev$
