In this paper, the magnetic dynamics and mechanical rotation about the center of mass of a uniaxial ferromagnetic fine particle in a viscous liquid are described using the classical approach. In particular, the synchronous rotation of the magnetization vector and unit vector, associated with the anisotropy axis, together with a circularly polarized external magnetic field is considered. The feature of this mode for the given system is that both the magnetization and anisotropy axis do not lie in the plane of the field polarization. This fact is explained by the presence of effective permanent field, perpendicular to the polarization plane. Obtained results allow to perform more realistic evaluations of the power loss of a external field interacting with a ferromagnetic fluid.