The conservation of momentum is most closely related to Newton's third law.
According to the conservation of momentum, momentum is neither created nor destroyed, although it can change from one form to another.
According to Newton's third law, for every action, there is an opposite reaction, and energy is neither created nor destroyed. Rather the energy is changed from the action to the reaction in a given system and the amount of energy remains the same.
Both the conservation of momentum and Newton's third law imply that energy in a system can be converted but the value remains the same in a system and hence is closely related.
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