Conservation of energy

Conservation of energy states that the total energy of an isolated system does not change. For a system that exchanges energy with its surroundings, the corresponding statement is a balance between stored energy and the transfers across the chosen boundary. The relevant system boundary and included forms of energy must therefore be specified.

For a constant-mass particle under a time-independent conservative force $\mathbf{F}=-\nabla U$, Newton's second law givesIts mechanical energy is conserved. With friction, that mechanical quantity generally decreases while internal energy or transfers to the surroundings account for the difference. A damped swinging body becoming stationary is therefore not a failure of conservation of energy. Richard Feynman introduces the principle through accounting for a quantity that can be hidden in different physical forms.^[ref]

The conservation of energy is a fundamental principle in physics that states that energy cannot be created or destroyed in an isolated system; it can only change forms. This means that the total energy of an isolated system remains constant over time, though it may transform from one type of energy to another, such as from kinetic energy (the energy of motion) to potential energy (stored energy based on position) or thermal energy (heat).