Problem 1.268

Demonstrate that in the reference frame rotating with a constant angular velocity \(\omega\) about a stationary axis a body of mass \(m\) experiences the resultant (a) centrifugal force of inertia \(\mathbf{F}_ {c f}=\) \(=m \omega^{2} \mathbf{R}_ {C},\) where \(\mathbf{R}_ {C}\) is the radius vector of the body's centre of inertia relative to the rotation axis; (b) Coriolis force \(\mathbf{F}_ {\text {cor }}=2 m\left[\mathbf{v}_ {c}^{\prime} \mathbf{\omega}\right],\) where \(\mathbf{v}_ {C}^{\prime}\) is the velocity of the body's centre of inertia in the rotating reference frame.