Question

Demonstrate that in the reference frame rotating with a constant angular velocity ω about a stationary axis a body of mass m experiences the resultant

(a) centrifugal force of inertia F_cf= mω²R_c, where R_c is the radius vector of the body's centre of inertia relative to the rotation axis;

(b) Coriolis force F_cor= 2m [v'_cω], where v'_c is the velocity of the body's centre of inertia in the rotating reference frame.

Answer 1

For a point mass of mass dm, looked at from C rotating frame, the equation is 

where vector r=radius vector in the rotating frame with respect to rotation axis and vector v=velocity in the same frame. The total centrifugal force is clearly

vector R_c is the radius vector of the C.M. of the body with respect to rotation axis, also