An annular body has an angle scale for measuring the rotational position of a machine part about an axis, the body having recesses and projections on its inner circumference, and at least one of the recesses being suited for a form-locking rotatably fixed attachment on the machine part. The sum of the central angles, which are respectively defined by starting points and end points of the projections is smaller than the sum of the central angles, which are respectively defined by the starting points and end points of the recesses. Such a body on a high-speed shaft of a machine tool may be used for measuring the rotational position of the shaft.