Apparatus for Determination of Residual Drag Torque on Small Spinning Spheres in Magnetic Suspension

An apparatus for measuring the frequency decay of magnetically suspended freely spinning steel spheres is presented. A residual drag torque, which considerably exceeds the gas friction torque in ultrahigh vacuum, has been determined by means of a new measuring system for small frequency changes, which features high resolution power even at low rotor speed. The decay ratio $\mathrm{-\omega ̇/\omega }$ has been recorded for several spheres with different diameters over a frequency range from 0.2 to about 10⁵ Hz. Apart from some characteristic deviations, which have been related to certain experimental conditions, a linear frequency dependence of the decay ratio ${\mathrm{-\omega ̇/\omega =a}}_0{\mathrm{+a}}_1\mathrm{r\omega }$ has been detected in the described apparatus (r being the sphere radius) with a₀≃3×10⁻⁹ sec⁻¹ and a₁≃3×10⁻¹² m⁻¹. An explanation is given for this type of drag torque. Measurements are reliable within ±6×10⁻¹¹ sec⁻¹ up to rω≃700 m/sec. Stabilities better than ±5×10⁻¹² sec⁻¹ during one day have been recorded. A long term stability of the latter magnitude is required to verify the existence of an ω⁶ proportional energy dissipation, which was deduced by Keith in 1963 from relativistic gravitational theories.