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

The change in angular position is equal to the area under the angular velocity versus time graph. Note that the area under the graph from t = 0 to t = 4 s is 60 rad. Therefore, $\theta = 60~rad$. We can express $\theta$ in units of revolutions: $\theta = (60~rad)(\frac{1~rev}{2\pi~rad})$ $\theta = 9.5~rev$ The object makes 9.5 revolutions during the first 4 seconds.