The relation between momentum conservation and Newton's third law revisited

Abstract

Under certain conditions usually fulfilled in classical mechanics, the principle of conservation of linear momentum and Newton's third law are equivalent. However, the demonstration of this 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 Newton's second law. On the other hand, under some additional conditions the combined laws of conservation of linear and angular momentum, are equivalent to 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 contained in Newton's second law is the clue.