# Lecture10 - Racquetball Striking a Wall Momentum and...

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Momentum and Impulse General Physics I Mechanics Racquetball Striking a Wall Physics 140 Mt. Etna Stewart Hall

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Conservation laws and symmetry What is the main reason the energy is conserved? Emmy Noether (1882-1935) showed that conservation laws are closely related to symmetries in space and time Specifically, if the laws of nature exhibit a symmetry, there will be a conserved quantity associated with this symmetry Time symmetry causes energy conservation Energy is conserved because the laws of nature do not change with time
Conservation laws and symmetry Today: another conservation law – conservation of momentum This law is also associated with a symmetry of the laws of nature Translational symmetry causes linear momentum conservation Momentum is conserved because the laws of nature are the same everywhere Every point in space is as good as any other (the same way as every moment of time is as good as any other) There will also be a third conservation law later on

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Are the laws of nature the same everywhere? Do they change? Symmetries are important, but how do we test them? Are the laws of nature the same everywhere Astrophysics tests this on the largest scales: The ability to look at distant objects allows us throughout the universe? Have the laws of nature always been the same? to look at physics very far from the Earth The finite speed of light allows us to see the past , probing physics through history So far these tests confirm translation and time symmetry
Momentum Kinetic energy is a scalar characteristic of the “quantity of motion”: Momentum is a vector characteristic of the “quantity of motion”: 2 2 1 mv KE = v m p r r = Measured in (kg m/s) Can re-write Newton’s 2

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