centre of mass

is: the point (not necessarily within the body) at which the entire mass of the body can be considered to be concentrated for the purpose of determining the translational motion of the body under an applied force. If the body is entirely free to move and the line of action of the force passes through the centre of mass, that force will cause translation of the centre of mass but not rotation about the centre of mass. [P2.3, P2.7, P2.8]

is determined: by considering the body to consist of (infinitesimal) mass elements at positions and then finding the point specified by such that

[M5.4]

should not be confused: with the centre of gravity.