Answer
(a) At t = 1 s: $\omega = 0$
(b) At t = 4 s: $\omega = -1.57~rad/s$
(c) At t = 7 s: $\omega = 9.42~rad/s$
Work Step by Step
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:
$\omega = \frac{\Delta \theta}{\Delta t}$
$\omega = \frac{(4\pi-(-2\pi))~rad}{2~s}$
$\omega = 9.42~rad/s$
