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The invariant quantities such as angular momentum, linear momentum and possibly energy (although that is generally considered thermodynamics) are all still conserved in special relativity.

What does happen however is that the equations for these invariants do change. For example, linear momentum according to Newton is simply mass times velocity but in Einstein's theory it becomes mass times velocity times a new thing called the gamma factor (which is almost equal to unity at low velocities so Newton did not detect it, but becomes very large close to the speed of light (the gamma factor is infinite at the speed of light)).

Special relativity also predicts the existence of spin which is related to angular momentum, but spin does not exist in Newton's theory.

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Q: What happens to Newtons laws of motion invariant quantities in special relativity?
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