We present the macroscopic dynamic description of a ferromagnetic nematic, where the nematic part and the magnetic part can move relative to each other. The relative velocity that describes such movements can be a slowly relaxing variable. Its couplings to the nematic and the magnetic degrees of freedom are particularly interesting since the symmetry properties (behavior under spatial inversion and time reversal) of the three vectorial quantities involved are all different. As a consequence, a number of new crosscouplings involving the relative velocity exist. Some of them are discussed in more detail. First, we demonstrate that transverse temperature gradients generate transverse relative velocities and, vice versa, that transverse relative velocities give rise to temperature gradients. Second, we show that a simple shear flow in the relative velocity with the preferred direction in the shear plane can lead in a stationary situation to a tilt of the magnetization.