Problem 1.269

A midpoint of a thin uniform rod $A B$ of mass $m$ and length $l$ is rigidly fixed to a rotation axle $O O^{\prime}$ as shown in Fig. 1.71. The rod is set into rotation with a constant angular velocity $\omega .$ Find the resultant moment of the centrifugal forces of inertia relative to the point $C$ in the reference frame fixed to the axle $O O^{\prime}$ and to the rod.