[UPSC IFoS 2010] Rotating Frame (Q154, 15M)

(i) For a particle of mass m moving with velocities \vec{v}_s and \vec{v}_r relative to the space and rotating axis, respectively, show that the equation of motion is obtained as \vec{F}-2m(\vec{\omega}\times\vec{v}_r)-m\vec{\omega}\times(\vec{\omega}\times\vec{r}) = m\vec{a}_r with \vec{\omega} and \vec{a}_r being the angular velocity and acceleration in rotating coordinates.