# Why isn't there such a thing as "internal momentum"?

The three most well-known conserved quantities in classical physics are energy, momentum, and angular momentum.

Suppose we have a system with no external forces acting on it. We can talk about the system's internal energy as the sum of all kinetic and potential energies of its particles and interactions between particles. If you think about subparts of the system, the internal energy is just what remains of the kinetic and potential energies when you consider the total system's center of mass reference frame (which is inertial because there are no external forces).

We can also talk about an analogue of this when it comes to angular momentum. The so-called spin angular momentum is what remains of the angular momentum of the when you consider the total system's center of mass reference frame.

Why isn't there an analogue of this for linear momentum?

• Why do you think that you cannot talk about the momentum of the parts internal to a system? Jan 31 at 23:38

Very simply, if we try to generalize the notion of an "internal $$x$$" of a system $$S$$ given any quantity $$x$$ by defining it to be the value of $$x$$ in the center of mass reference frame of system $$S$$, then "internal momentum" is always going to be zero, because the total momentum of a system $$S$$ in the center of mass reference frame of $$S$$ is always zero. This renders the concept of "internal momentum" trivial and uninteresting. As far as I can tell, there isn't anything deeper than that (although others can provide their own answers if they disagree).