# Are principle of Conservation of energy and principle of conservation of momentum consequences of Newton's laws?

It is known that principle of Conservation of momentum and principle of conservation of energy are two fundamental principles of physics.But in RP Feynman's Lectures of physics, in the chapter of conservation of momentum, it is said that conservation of energy and conservation of momentum are consequences of Newtons laws of dynamics.Is it correct?

• A good answer is given here by Ben for a similar question. physics.stackexchange.com/q/77465 . – anna v Sep 16 '13 at 4:24
• Note that Newton's laws don't deal with all the phenomena in physics, e.g., light. Therefore it would only make sense to discuss their equivalence to conservation laws within a very limited context, essentially mechanics and Newtonian gravity. – Ben Crowell Sep 16 '13 at 19:27

Using Newton's Laws as a starting point, they are a consequence. Actually, Newton spoke in terms of momentum. Newton's 2nd Law actually says that force is equal to the change in momentum over time (which reduces to $F=ma$ if mass is constant). Newton's 3rd Law basically gives us conservation of momentum. If two objects impart equal and opposite forces on one another, for the same amount of time, then their change in momentum will also be equal and opposite.
Energy also traces back to Newton's Laws. A combination of the definition of work ($W = F \cdot \Delta x$), the Work-Energy theorem ($W _{net} = \Delta KE$), total energy ($E = KE + PE$), and ($F = -\Delta PE/\Delta x$) will show the conservation of energy. Alternatively, if you accelerate a mass with gravity and compare the kinetic and gravitational potential energy, or a spring-mass system and compare the kinetic and elastic potential energy, you will see that they are indeed conserved.
On the other hand, the 1st Law of Thermodynamics gives us the conservation of energy independent of Newton. Furthermore, both energy and momentum are conserved in quantum mechanics, where $F=ma$ is meaningless. With that in mind, we might say that Newton's Laws (stated as regarding forces) may be a consequence of our conservation laws, not the other way around.