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What conditions? If you look carefully at the impulse-momentum equation,
it becomes apparent that:
This is one way to state the Law of Conservation of Momentum. It follows directly from the impulse-momentum equation, which is, essentially, Newton's Second Law. (Here is a more direct way to get the Law of Conservation of Momentum from Newton's Second Law.) However, the Law of Conservation of Momentum is much more powerful than Newton's Second Law. No experiment to date has shown a violation of the Law of Conservation of Momentum. It applies to objects moving very fast or to objects inside the atom - both places where Newton's Second Law fails.
In addition to its universal applicability, the Law of Conservation of Momentum is a very powerful, and maybe even better, simple and straightforward way to explain the physics of many situations.