A power-off brake for stopping a rotating shaft comprises a solenoid including a coil and armature, an opposing plate axially spaced from the armature, and a ball carrier rotor between the armature and opposing plate. The ball carrier rotor rotates with the shaft and carries spherical balls in recesses angularly space about the shaft. The armature and opposing plate have respective braking surfaces. In one embodiment, at least one braking surface is ramped to urge the plurality of balls radially outward against an internal surface of a surrounding outer race as the armature is forced toward the opposing plate under spring loading when current to the solenoid coil is shut off. In another embodiment, the braking surfaces are not ramped, such that the balls are merely clamped between the braking surfaces upon solenoid deactivation. Increased rolling friction stops rotation of the ball carrier rotor and the shaft without problematic wear.