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

(a) At t = 1 s: $\omega = 0$ (b) At t = 4 s: $\omega = -1.57~rad/s$ (c) At t = 7 s: $\omega = 9.42~rad/s$
The angular velocity is the slope of the angular position versus time graph. (a) We can find the slope between t = 0 and t = 2 s: $\omega = \frac{\Delta \theta}{\Delta t}$ $\omega = \frac{0}{2~s}$ $\omega = 0$ (b) We can find the slope between t = 2 s and t = 6 s: $\omega = \frac{\Delta \theta}{\Delta t}$ $\omega = \frac{(-2\pi-0)~rad}{4~s}$ $\omega = -1.57~rad/s$ (c) We can find the slope between t = 6 s and t = 8 s: $\omega = \frac{\Delta \theta}{\Delta t}$ $\omega = \frac{(4\pi-(-2\pi))~rad}{2~s}$ $\omega = 9.42~rad/s$