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 wafer carrier rotor is contained by a set of idlers that are attached to a stationary rotor housing to provide support against abrading forces that are imposed on the wafer by the moving abrasivecoating on a rotary platen. 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 system is also well suited for lapping optical devices and rotary seals and for chemical mechanical planarization (CMP) polishing of wafers using resilient pads. Pressurized air is injected into the bellows device to provide uniform abrading pressure across the full surface of the wafer. Wafers can be attached to the workpiece carrier with vacuum.