Answer
2.4 radians/sec
Work Step by Step
If $P$ is a point moving with uniform circular motion on a circle of radius $r$, and the line from the center of the circle through $P$ sweeps out a central angle $\theta$ in an amount of time $t$, then the angular velocity, $\omega$ (omega), of $P$ is calculated as $\omega=\frac{\theta}{t}$.
We are given that $\theta=12\pi$ radians and $t=5\pi$ sec.
Therefore, $\omega=\frac{12\pi radians}{5\pi sec}=\frac{12\pi radians\div\pi}{5\pi sec\div\pi}=\frac{12radians}{5sec}=2.4$ radians/sec.
