Lecture 20: Angular Momentum Vector and Precession

1. Lecture 20: Angular Momentum Vector and Precession Today’s Concepts: Angular Momentum Precession

2. This is really what today’s class is about!

3. ACT A puck slides in a circular path on a horizontal frictionless table. It is held at a constant radius by a string threaded through a frictionless hole at the center of the table. If you pull on the string such that the radius decreases by a factor of 2, by what factor does the angular velocity of the puck change? A)2B)1C) 4 D) 1/2

4. ACT answer R Since the string is pulled through a hole at the center of rotation, there is no torque: Angular momentum is conserved. =

5. ACT A puck slides in a circular path on a horizontal frictionless table. It is held at a constant radius by a string threaded through a frictionless hole at the center of the table. If you pull on the string such that the radius decreases by a factor of 2, by what factor does the kinetic energy of the puck change? A)2B)1C) 4 D) 1/2

6. ACT answer R Angular momentum is conserved:

7. Where does the “extra” energy come from? (Work-Kinetic Energy Theorem) Conservation of L:

8. There are no external torques acting on the student-stool system, so angular momentum will be conserved: Initially:Li= Ii ωi Finally:Lf= If ωf ωf ωi Ii If Li Lf

9. Where does the “extra” kinetic energy come from? Since the student has to force her arms to move toward her body, she must be doing positive work! ωf ωi (Work-Kinetic Energy Theorem) Ii If Li Lf

10. Food for thought R We just used to find But So how do we get an αwithout a τ?

11. Food for thought Now suppose τEXT= 0: So in this case we can have an αwith no external torque!

12. Vector Nature of Angular Momentum

13. CheckPoint: Precession Direction A disk is spinning with angular velocity ωon a pivoted horizontal axle as shown. Gravity acts down. In which direction does precession cause the disk to move? A) Out of the page B) Into the page C) Up D) Down

14. Precession The magnitude of the torque about the pivot is τ=Mgd. The direction of this torque at the instant shown is out of the page (using the right hand rule). The change in angular momentum at the instant shown must also be out of the page!

15. Precession τEXT Ω Aerial View pivot dϕ Precession frequency

16. Precession In this example: Direction: The tip of Lmoves in the direction of τ.

17. ACT In which direction does point? B A

18. CheckPointRevote In which direction does precession cause the disk to move? Into the page Out of the page Up Down Torque is out of the page

19. CheckPoint: Precession Speed 1 A disk is spinning with angular velocity ωon a pivoted horizontal axle as shown. Gravity acts down and the disk has a precession frequency Ω. If the mass of the disk were doubled but its radius and angular velocity were kept the same, the precession frequency would: A) Increase B) Decrease C) Stay the same About 45% of you got this correct

20. CheckPoint Results: Precession Speed 1 If the mass of the disk were doubled but its radius and angular velocity were kept the same, the precession frequency would: A) Increase B) Decrease C) Stay the same

21. CheckPoint revote: Precession Speed 2 A disk is spinning with angular velocity ωon a pivoted horizontal axle as shown. Gravity acts down and the disk has a precession frequency Ω. If the radius of the disk were doubled but its mass and angular velocity were kept the same, the precession frequency would A) Increase B) Decrease C) Stay the same

22. Wheel steers left Wheel steers right A challenge!!! “All of this stuff doesn't really seem practical. If you can't prove me wrong then we should all just get A's for this course.” http://www.youtube.com/watch?v=cquvA_IpEsA(see 3:00) Practical Application: Keeps you from falling off your bike when you rideusing no hands! Riding straight(τ = 0) Lean Left(τ out of page) Lean Right(τ into page) Wheel steers straight

23. d Mg

24. L (using right hand rule)