Answer
In case 1, $~~\omega = 0~~$ before $~~t = 0$
In case 2, $~~\omega = 0~~$ at $~~t = 0$
In case 3, $~~\omega = 0~~$ after $t = 0$
Work Step by Step
$\omega = \frac{d\theta}{dt}$
Then $~~\omega = 0~~$ when the slope of the $\theta$ versus $t$ curve is zero.
In case 1, we can see that the slope of the $\theta$ versus $t$ curve is zero when $t \lt 0$
Thus, in case 1, $~~\omega = 0~~$ before $~~t = 0$
In case 2, we can see that the slope of the $\theta$ versus $t$ curve is zero when $t = 0$
Thus, in case 2, $~~\omega = 0~~$ at $~~t = 0$
In case 3, we can see that the slope of the $\theta$ versus $t$ curve is zero when $t \gt 0$
Thus, in case 3, $~~\omega = 0~~$ after $t = 0$
