On the motion of the centre of mass of a system of particles

We consider the simple and classical theorem of the motion of the centre of mass, pointing out that many textbooks append a wrong corollary to it: that the motion of the centre of mass is always independent from the internal forces. We give an explicit example showing that this corollary is wrong. We discuss using a historical approach the genesis of such a misunderstanding. The contents of the paper may be used at different levels of complexity. The explicit example may be used to discuss the theorem at an undergraduate level in a clearer way than usual, but the paper also contains much for an advanced course on classical mechanics. Moreover, the historical approach may also be of interest in the study of the philosophy and sociology of science.