Answer
The DVD makes a total of 37.5 revolutions.
Work Step by Step
We can use the average angular velocity to find the number of revolutions in the first 1.0 second.
$\theta_1 = (\frac{\omega_f+\omega_0}{2})(t)$
$\theta_1 = (\frac{500~rpm+0}{2})(\frac{1.0}{60}~min)$
$\theta_1 = \frac{25}{6}~rev$
We can find the number of revolutions in the next 3 seconds.
$\theta_2 = \omega_f~t$
$\theta_2 = (500~rpm)(\frac{3.0}{60}~min)$
$\theta_2 = 25~rev$
We can use the average angular velocity to find the number of revolutions in the final 2.0 seconds.
$\theta_3 = (\frac{\omega_f+\omega_0}{2})(t)$
$\theta_3 = (\frac{500~rpm+0}{2})(\frac{2.0}{60}~min)$
$\theta_3 = \frac{25}{3}~rev$
We can find the total number of revolutions.
$\theta = \theta_1+\theta_2+\theta_3$
$\theta = \frac{25}{6}~rev+25~rev+\frac{25}{3}~rev$
$\theta = 37.5~rev$
The DVD makes a total of 37.5 revolutions.
