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.