1. -Angular Momentum of a Rigid Object -Conservation of Angular Momentum AP Physics C Mrs. Coyle

2. Angular Momentum of a Particle on Rotating Rigid Object For a particle of mass m i of the object as shown  L i = r i m i v i = m i r i 2  L and  vectors are perpendicular to the xy plane.

3. Angular Momentum of a Rotating Rigid Object The angular momentum of the entire object, is the sum of the angular momentum vectors of all the individual particles

4. Rotational Form of Newton’s Second Law

5. Note: The rotational form of Newton’s Second Law is also valid for a rigid object rotating about a moving axis provided the moving axis: (1) passes through the center of mass (2) is an axis of symmetry

6. Angular Momentum of a Bowling Ball I=2/5MR 2 L z = I  The direction of the angular momentum is in the positive z direction

7. Conservation of Angular Momentum In the absence of a net external torque (the system is isolated) the net angular momentum of a system is conserved. L i = L f I i  i = I f  f

8. Remember: Closed System: A system that has no gain nor loss of mass. Isolated System: A closed system with no net external force acting on it.

9. I i  i = I f  f Why does the skater spin faster when she pulls together her arms?

10. Video Link: Gyroscope http://www.youtube.com/watch?v=cquvA_Ip EsA&NR=1 http://www.youtube.com/watch?v=cquvA_Ip EsA&NR=1 Bicycle Wheel Gyroscope (M.I.T. Physics) http://www.youtube.com/watch?v=8H98BgRz pOM&NR=1 http://www.youtube.com/watch?v=8H98BgRz pOM&NR=1

11. Gyroscope

12. Ex: Conservation of Angular Momentum

13. Video Link: Conservation of Angular Momentum (Bicycle Wheel) http://www.youtube.com/watch?v=UZlW1a63 KZs&NR=1 http://www.youtube.com/watch?v=UZlW1a63 KZs&NR=1

14. Note: For an isolated system: Energy, Linear Momentum, and Angular Momentum are conserved.

15. What happens to the angular speed of the system as the person moves towards the center of the Merry-Go- Round? Σ I i  i = Σ I f  f

16. Why does the kinetic energy of the system increase when the person moves towards the center?

17. Motion of a Top Precessional Motion : the motion of the axis of symmetry.

18. Angular Momentum of a Molecule

19. Ex: #30 A student sits on a freely rotating stool holding two 3kg masses. When his arms are extended horizontally, the masses are 1m from the axis of rotation and he rotates with an angular speed of 0.750rad/s. The moment of inertia of the student plus stool is 3kg m 2 and is assumed constant. The student pulls the weights inward horizontally to a position 0.3m from the rotation axis. a) Find the new angular speed of the student, b) The kinetic energy of the rotating system before and after he pulls the weights inwards. Ans: a) 1.91rad/s, b)2.53J, 6.44J