Flat-surfaced workpieces such as semiconductor wafers are attached to a rotatable floating workpiece holder carrier rotor that is supported by and rotationally driven by a bellows. The rotating wafer carrier rotor is restrained by a set of idlers that are attached to a stationary housing to provide rigid support against abrading forces. The idlers allow low-friction operation of the abrading system to be provided at the very high abrading speeds used in high speed flat lapping with raised-island abrasive disks. The carrier rotor is also restrained by a rigid rotating housing to allow a limited lateral motion and also a limited angular motion. Air pressure within a sealed bellows chamber provides controlled abrading pressure for wafers or other workpieces. Vacuum can also be applied to the bellows chamber to quickly move the wafer away from the abrading surface. Wafers can be quickly attached to the workpiece carrier with vacuum.