The relation between momentum conservation and the Newton’s third law revisited

Under certain conditions usually fulfilled in classical mechanics, the principle of conservation of linear momentum and the Newton’s third law are equivalent. However, the demonstration of such fact is usually incomplete in textbooks. We shall show here that to demonstrate the equivalence, we require the explicit use of the principle of superposition contained in the Newton’s second law. On the other hand, under some additional conditions the combined laws of linear and angular momentum conservation, are equivalent to the Newton’s third law with central forces. The conditions for such equivalence apply in many scenarios of classical mechanics, once again the principle of superposition of the Newton’s second law is the clue. PACS: {01.30.Pp, 01.55.+b, 45.20.Dd}