## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

The area under the $\omega$ versus time graph is equal to $\theta$, the total angle through which the particle moves: $\theta = (20~rad/s)(2~s)+(10~rad/s)(2~s)$ $\theta = 60~rad$ We can convert the angle $\theta$ to revolutions; $\theta = (60~rad)(\frac{1~rev}{2\pi~rad})$ $\theta = 9.5~rev$ The particle makes 9.5 revolutions during the first 4 seconds.