[UPSC IFoS 2012] Rotating Frame (Q150, 10M)

Using the concept of the operator equation for a given vector quantity of a rotating body, show that \vec{v}_s = \vec{v}_r + \vec{\omega} \times \vec{r} where \vec{v}_s and \vec{v}_r are the velocities of the particle relative to space and rotating sets of axes while \vec{\omega} is the angular velocity of the earth relative to the inertial system. Obtain the expression for the Coriolis force for such a moving system of mass m.