Flat-surfaced workpieces such as semiconductor wafers or sapphire disks are attached to a rotatable floating workpiece holder carrier that is supported by a pressurized-air flexible elastomer sealed air-chamber device and is rotationally driven by a circular flexible-arm device. 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 abrading system can be operated at the very high abrading speeds used in high speed flat lapping with raised-island abrasive disks. The range of abrading pressures is large and the device can provide a wide range of torque to rotate the workholder. Vacuum can also be applied to the elastomer chamber to quickly move the wafer away from the abrading surface. Internal constraints limit the axial and lateral motion of the workholder. Wafers can be quickly attached to the workpiece carrier with vacuum.