Closed Systems vs. Open Systems
A closed system refers to a system that doesn’t lose mass, energy, charge, etc so conserved quantities are considered to be constant. On the other hand, an open system refers to exchanges of energy, charge, etc with the object(s) surroundings.
Open systems may seem to violate conservation of mass, charge, matter, and energy since the amount of the previously stated quantities can increase or decrease without replacement.
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Momentum of a System
In terms of momentum of a system, internal forces, like all forces, always occur in action reaction pairs. Since the forces in action reaction pairs are equal and opposite due to Newton’s 3rd law, internal forces must always sum to zero. If the internal forces cancel, that means that the sum of the total forces must simply be all of the external forces. External forces could sum to zero but that won’t always be the case.
The change in net momentum is directly related to the net external force. If the net external force acting on a system is equal to zero, then its net momentum is conserved so pinitial = pfinal. This only applies to the net momentum of a system, not individual momenta of each object.