## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th 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 convert $\theta$ to 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.