Relative changes of inductance &Dgr;L/Lof a single layer coil surrounding a thin electrically conducting disk which can rotate about an axis perpendicular to the coil axis are studied experimentally as a means of measuring angular displacements. &Dgr;L/Lis found to be a strong function of disk diameter and is weakly dependent on the ratio of disk thickness to electromagnetic skin depth when this ratio is of the order unity. Values of &Dgr;L/Las a function of disk diameter are given for lead, brass and copper. Detection sensitivities using a resonant tank circuit or an astatic transformer are given in terms of &Dgr;L/Land it is shown that sensitivities of the order of 10−3to 10−4deg are practical. Application of this system to the Rayleigh disk and cryogenic environments are emphasized and an expression for the magnetic torque due to detection currents is given.