Some Things Never Change! i)Momentum ii)Angular Momentum iii)Energy iv)Charge, etc

Conservation of Momentum In the absence of an external force, the total linear momentum of a system remains constant. Before Collision After Collision v 1i v 2i v 1f v 2f m1m1 m2m2

Impulse = change in momentum F Newton’s 3 rd : final momentum = initial momentum Conserved!

Is momentum conserved if you jump up from the earth? What about a Mexican jumping bean? Problem: A canon of mass 100 kg is initially at rest and fires a 1 kg canonball with speed 75 m/s horizontally. What is the recoil velocity of the canon? M m Demo of carts on track

Gun aimed downward Total momentum zero mV Mv

Molecular bullets

Conservation of Angular Momentum For point mass around circle, If there are no external torques, angular momentum is conserved. R r

Conservation of Energy The total energy of an isolated system is always conserved. Conservative forces: work done by conservative force is independent of path taken. A B Allow you to define potential energy.

If you have only conservative forces, then the sum of potential and kinetic energy is conserved. For gravity near earth’s surface,

Roller coaster 10 m 5 m 8 m ABCD If initially at rest at A, what is speed at B, C, D?

Other conservation laws: Conservation of Baryon number (nucleon number): Baryons interact via strong nuclear force, e.g. protons and neutrons. Conservation of electric charge

Possible particle reaction: B = = Conservation of Lepton number Leptons interact via weak nuclear force, e.g., electrons and neutrinos. Neutron decay L = 0 =