1. Newton’s Laws 1.An object that is in motion will stay in motion and an object that is at rest will stay at rest unless acted on by an external force. 2.F=ma. 3.For every action there is an opposite and equal reaction.

2. Third Law For every action there is an opposite and equal reaction. Leads to momentum conservation One of the pillars of modern physics

3. Energy Conservation Energy Conservation: Newton’s second law

4. Lagrangian Formulation Lagrangian invariant in spaceMomentum Conservation Lagrangian invariant in timeEnergy Conservation Attempt to keep these invariance principles to keep conservation of energy and momentum H=Energy=constant

5. Galilean Invariance An inertial frame is any coordinate system where the following holds: Galilean Invariance: If one coordinate systems is moving at constant velocity to an inertia frame, then the new coordinate system is an inertia frame. Force is the same in the two frames!

6. Ball in a Moving Car Ball: Person:

7. Ball in a Moving Car (continued) x0x0 vxvx Ball: Person: x0x0 Parabola

8. Ball in a Moving Car Ball: Person 2:

9. Ball in a Moving Car (continued) d vxvx Ball: Person: vxtvxt

10. What Does Galilean Invariance Mean? Energy conservation Momentum conservation Universal F independent of frame

11. Violations of Galilean Invariance Accelerated reference frames: (momentum and energy not conserved) Time not universal: Frame dependence of constants (scalers):