Suppose we take the three Newton’s Laws as axioms. Existence of inertial reference frames F = ma F(A on B) = -F(B on A) Also suppose also we are considering purely classical mechanical processes on point particles (no heat transfer, etc.). It is clear to me that the conservation of momentum directly follows from Newton's Laws. (If a force is the time rate of momentum transfer and forces come in pairs, then the momentum increase caused by one force is balanced by the momentum decrease caused by its reaction force.) But here are my questions: If I take Newton's Laws as axioms, is the conservation of energy a derivable theorem or an independent axiom? In other words, does the conservation of energy directly follow from Newton's Laws just like the conservation of momentum does? Are equations written for the conservation of energy and conservation of momentum independent? (I.E. are they merely two representations of the same thing, or does one give additional information over the other?) From what little I know about more advanced physics, I have a feeling that the two are independent (since energy and linear momentum conservations are consequences of spatial and time invariance). I was hoping someone could give me more insight on the matter. Thanks!