Answer
See the explanation below.
Work Step by Step
The angular velocity of the point is $\frac{\pi }{12}$ radians per hour, which means that the point rotates $\frac{\pi }{12}$ radians in one hour.
The rotation of the point in 24 hours is
$\begin{align}
& \left( 24 \right)\frac{\pi }{12}\ \text{rad}=\frac{24\pi }{12}\ \text{rad} \\
& =2\pi \ \text{rad}
\end{align}$
Hence, the point will complete one full revolution in 24 hours because $2\pi $ radians is the measure of one full revolution.
