# Chapter 4 - Kinematics in Two Dimensions - Exercises and Problems - Page 107: 43

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.

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