Answer
$1.8\times 10^{3}rad$
Work Step by Step
Angular velocity $\omega=120 rad/s$ and angular acceleration $a =4 rad/sec^{2}$.
Let angular displacement before stopping be $\Delta\theta$.
Time taken to stop is $30sec$ (from $\omega_{f}=\omega_{i}+at$) [ ..as found from previous question].
So, by rotaional kinematics equation:
$\Delta\theta=\omega_{i}t+\frac{1}{2} at^{2}$
We get:$0=0.5*4*30*30$
=> $s=1800 rad=1.8\times10^{3}rad$
