This rolling bearing assembly comprises a rolling bearing with an inner ring, an outer ring and several rolling bodies between the inner and outer rings, at least one sensor adapted to detect a rotation parameter of a first ring with respect to a second ring of the rolling bearing and a support member holding the sensor in position with respect to the rolling bearing. The spacer layer, on an air bearing surface, has a larger film thickness at both side edge parts in a track width direction than a film thickness at a central part in a track width direction. The resilient assembly is mounted slidably in the channel of the post and has two friction feet and a coil spring. When the rotation axis of the drill positioned perpendicular to the surface of the workpiece is tilted to an angle equal to or greater than a predetermined angle, the tilt sensor senses the tilt to shutoff a drive current of the electric drill.