Answer
2.667 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 $\theta=8\pi$ radians and $t=3\pi$ sec.
Therefore, $\omega=\frac{8\pi radians}{3\pi sec}=\frac{8\pi radians\div\pi}{3\pi sec\div\pi}=\frac{8radians}{3sec}\approx2.667$ radians/sec.
