We address the theory of the coupled lattice and magnetization dynamics of freely suspended single-domain nanoparticles. Magnetic anisotropy generates low-frequency satellite peaks in the microwave absorption spectrum and a blueshift of the ferromagnetic resonance (FMR) frequency. The low-frequency resonances are very sharp with maxima exceeding that of the FMR, because their magnetic and mechanical precessions are locked, thereby suppressing the effective Gilbert damping. Magnetic nanoparticles can operate as nearly ideal motors that convert electromagnetic into mechanical energy. The Barnett damping term is essential for obtaining physically meaningful results.