I'm reading Susskind's Classical Mechanics: The Theroretical Minimum and I also like to restrict my question to classical mechanics:
In chapter 4, momentum conservation is shown for a set of particles. In chapter 5 energy conservation is shown for a body in free fall towards Earth (potential energy decreases, kinetic energy increases). The authors then point out that energy conservation holds here in the free falling body example, but not conservation of momentum, and the reason is that we neglected the Earth. When considering the change of Earth's momentum (which starts to move to the falling body as well as actio = reactio), the sum of Earth's and free falling body's momentum is of course conserved.
This leads me to the question what the preconditions for applying momentum and energy conservation in mechanics are? Seems that momentum conservation needs a closed system to be true, but energy conservation not, because we don't have to consider the change of the Earth's potential energy with respect to the falling body, nor the Earth's kinetic energy towards the small body, to argue that the sum of all energies for body + Earth is constant (like we argue with the momentum...).