1. PHY221 Ch19/20: Angular Momentum 1.Main Points: Definition Proof dL/dt=  Proof L=I  for a rigid body Conservation of L 2.Examples Person running and jumping on merry-go-round Skater Gravity on Planet Sun

2. PHY221 Ch19/20 : Angular Momentum 1. Main Points Definition of: or for N particles: Proof: Follow parallel with introduction of momentum in translational description: As before we’ll only consider motion in a plane and thus all rotational quantities are vectors along same direction which is the axis perpendicular to that plane => we don’t worry about vectors!

3. PHY221 Ch19/20: Angular Momentum 1. Main Points Proof of L=I  for a rigid body ( I =constant) by using  = I  Conservation of L when no external torque We assume internal Action/Reaction forces to act on the same line (not just direction)

4. PHY221 Ch19/20 : Angular Momentum 2. Discuss Example: Person jumps on merry-go-round: given m, M and vo what is the final w of person +merry-go-round

5. PHY221 Ch19/20 : Angular Momentum 2. Discuss Example: Skater

6. PHY221 Ch19/20 : Angular Momentum 2. Discuss Example: Planet around Sun. Prove conservation of L by showing  =0

7. PHY221 Ch20: Angular Momentum 2. Discuss Example: Mass pulled by a central string Energy consideration when string is pulled in: Torque and angular momentum:

8. PHY221 Ch20: Angular Momentum 2. Discuss Example: Perpendicular  and L  L precession Gyroscope: start with spinning top held at both ends and remove one end:

9. PHY221 Ch19: Angular Momentum 2. Discuss