In vibrational theory, the motion of a polyatomic molecule is usually initially regarded as the independent superposition of a rotation and a vibration, with the vibration considered in a coordinate system that rotates with the molecule. This initial treatment must be corrected for centrifugal forces and for Coriolis forces. The Coriolis force on an atom is given by \(F_{\rm{Coriolis}} = 2m v_{\rm{a}} \omega \sin \varphi\), where \(m\) is the mass of the atom, \(v_{\rm{a}}\) is its apparent velocity in the rotating coordinate system, \(\omega\) is the angular velocity of the coordinate system, and \(\varphi\) is the angle between the velocity vector and the axis of rotation.