In physics, a conservation law states that, for an isolated system, a particular physical quantity does not change for the system as a whole as it evolves in time.  At this point in the course, we have seen three major conservation laws:

• Conservation of energy
• Conservation of (linear) momentum, and
• Conservation of angular momentum

All three of these conservation laws can be used as powerful tools to keep track of the pieces of an isolated system as they interact with each other.

But beyond their importance as principles of nature, each of these conservation laws points to an underlying symmetry that seems to govern the universe in which we live.  Conservation of energy is related to the time invariance of physical systems, meaning that running an experiment now or running the same experiment in an hour won’t change the results of the experiment.  When you choose to start doesn’t affect the results.  Conservation of linear momentum is related to the translational invariance of physical systems.  If you have a lab space in a long building that is 100 m across, the results of an experiment won’t depend on whether you set up the experimental apparatus one end of the lab or the other.  Conservation of angular momentum is related to the rotational invariance of physical systems.  If you set up your experiment and run it, then turn your apparatus through some angle (say 90 degrees) and run it again, you will still get the same results.  The fact that we live in a world where the physics doesn’t change if you slide your experiment back and forth in time, slide it back and forth in space, or rotate it about a spatial axis is connected to the fact that energy, momentum, and angular momentum are conserved for isolated systems.