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.