# When does the conservation of linear momentum hold?

I have a few basic questions about conservation of linear momentum:

When the example of particle colliding in a 3D box are used to explain conservation of linear momentum, do we assume that the system is completely isolated? If so, then then total energy of the system must remain constant.

In my understanding, we assume that the system cannot transfer energy in ANY other form (such as sound, radiation) other than changes in kinetic energy. However, do we also assume that the system is not placed inside any potential fields (such as gravitational potential fields)? Therefore, unable to lose PE also?

Ultimately, these constraints on the system mean that the only energy transfer between the particles can be in the form of changes in kinetic energy.

Additionally, when we can use the assumption that the conservation of linear momentum applies to a system of interest? Should the system be arranged such that the only changes in energy are changes in KE? and changes in PE, sound energy etc. are negligible?

• It is up to you what you assume. – my2cts Jan 16 '20 at 22:49

Momentum is always conserved. Energy is always conserved.

Since momentum is always conserved, it's irrelevant what's going on with kinetic energy. If you were considering energy conservation, then you would just want to keep in mind that kinetic energy isn't conserved -- the total energy is.

If a system is not isolated, then you can't just count that system by itself and expect conservation laws to hold.

Conservation of Momentum

Momentum of a system is conserved whenever the net external force acting on the system is $$0$$.

Conservation of Energy

Energy is conserved whenever the net work done by external forces are zero i.e., there is no exchange of energy from outside.

Note that the conservation laws are independent of one another.