Different textbooks of Mechanics give solely composition of accelerations where motion of moving frame of coordinates is rotation about a fixed axis and translation. This paper has developed the Theorem of Composition of Accelerations of Moving frame in plane Motion. We obtain a set of differ-antial equations which are available to be solved on digital computer.

The question how to choose the centroid in the theorem of the angular momentum has been discussed for thirty years(see references [1]~[4]). This paper gives a unified statement of the theorems of the change in the angular momentum of a system of particles. Especially, We develop the theorem of the angular momentum of a system of particles with respect to the centre of instontaneous zero velocity, in general, it is considered impossible.Using this theorem, we solve an example, the solution of which in this way was considered impossible.