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Centre of Mass Velocity

If we calculate the total momentum of a composite system and then divide by the total mass, we obtain the velocity of the system-as-a-whole, which we call the velocity of the centre of mass. If we imagine ``running alongside'' the system at this velocity we will be ``in a reference frame moving with the centre of mass,'' where everything moves together and bounces apart [or whatever] with a very satisfying symmetry. Regardless of the internal forces of collisions, etc., the centre of mass [CM] will be motionless in this reference frame. This has many convenient features, especially for calculations, and has the advantage that the inifinite number of other possible reference frames can all agree upon a common description in terms of the CM. Where exactly is the CM of a system? Well, wait a bit until we have defined torques and rigid bodies, and then it will be easy to show how to find the CM.