The RSM can be used to detect magnetic moment (vM≥5×10−6emu), rotational hysteresis (vWR/H≥10−2emu), spin flop (vM≥5×10−5emu), and properties related to anisotropy energy [vK/H, v(&khgr;⊥−&khgr;∥)HandvMx≥5×10−6emu], i.e., anisotropy constants, anisotropic susceptibility, and anisotropic spontaneous magnetization. Samples are either symmetric about, or offset from, an axis of rotation which is set parallel or perpendicular to an applied dc field. Coils are oriented to sense magnetization along or normal to the field axis. For measuring specific parameters, a phase sensitive detector, an electronic integrator, or an oscilloscope is employed. Detailed expressions relating magnetic properties and signal output are presented, along with illustrative experimental results.