Answer
(a) At t = 1 s:
$\omega = 6.3~rad/s$
(b) At t = 4 s:
$\omega = 0$
(c) At t = 7 s:
$\omega = -6.3~rad/s$
Work Step by Step
The angular velocity is the slope of the angular position versus time graph.
(a) At t = 1 s:
$\omega = \frac{\Delta \theta}{\Delta t}$
$\omega = \frac{4\pi~rad}{2~s}$
$\omega = 6.3~rad/s$
(b) At t = 4 s:
$\omega = 0$
(c) At t = 7 s:
$\omega = \frac{\Delta \theta}{\Delta t}$
$\omega = \frac{(-2\pi-4\pi)~rad}{3~s}$
$\omega = -6.3~rad/s$
