Answer
$\omega = \frac{mgr}{L }$
Work Step by Step
Examining the values of omega and the angular displacement, we find the following equation:
$\omega = \frac{\Delta L}{Lsin\theta \Delta t}$
We know that the value of torque is $\tau=\frac{\Delta L}{\Delta t}$. Thus:
$\omega = \frac{\tau}{Lsin\theta }$
Using the definition of torque as well as the fact that the force acting is gravity, which equals mg, it follows:
$\omega = \frac{mgrsin\theta}{Lsin\theta }$
$\omega = \frac{mgr}{L }$
