When does Newton's Second Law not hold?

[Delta2]

It is just an abstract point. There is no "material center of mass".

And how do you refer to the point of matter that lies in the spatial coordinates of the geometric c.o.m? (there might be the case that there is no matter there but the usual case is that there is).

I ve to say, though i cannot prove it, my intuition tells me that the velocity of the material c.o.m (in the usual case it exists) and the geometric c.o.m is the same in all cases except in the case there is asymmetry in the way that mass is gained or lost.

 

[Jano L.]

And how do you refer to the point of matter that lies in the spatial coordinates of the geometric c.o.m? (there might be the case that there is no matter there but the usual case is that there is).

I do not know any special name for it. The material point is not important.

I ve to say, though i cannot prove it, my intuition tells me that the velocity of the material c.o.m (in the usual case it exists) and the geometric c.o.m is the same in all cases except in the case there is asymmetry in the way that mass is gained or lost.

That is true for rigid bodies. If the parts move with respect to each other, the center of mass of the body may move as well and is not attached to any particular mass point.