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 $F_{\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{l}\mathrm{i}\mathrm{s}}=2m{v}_{\mathrm{a}}\omega \sin \phi$, where $m$ is the mass of the atom, $v_{\mathrm{a}}$ is its apparent velocity in the rotating coordinate system, $\omega$ is the angular velocity of the coordinate system, and $\phi$ is the angle between the velocity vector and the axis of rotation.