On some important feature of the angular momentum of a rigid body in pure rotation about mass center

In this paper we prove that the angular momentum of a rigid body performing a pure rotation about fixed mass center does not depend on the reference point, thus it may be considered as a natural measure of the amount of rotational motion. This implies also (somewhat forgotten) decomposition of the angular momentum of a rigid body in a general motion onto spin and orbital angular momenta. The canonical forms of definitions of three fundamental quantities: linear momentum, angular momentum and kinetic energy are presented in this context, emphasizing the specific role of the mass center. Various formulas for the angular momentum are discussed and their practical usefulness is analyzed. There is also shown some lack of clarity in interpretation of the physical meaning of this quantity, which may be a source of problems, especially in teaching the classical mechanics on a basic university level.