1. Angular Momentum of a rigid object rotating about a fixed axis But for any rigid object the rotational inertia is a constant Newton’s Second Law Analogous to

2. What if the system is isolated and closed? Isolated – no external torques Closed – no change in the mass Law of Conservation of Angular Momentum In any closed, isolated system, the angular momentum is constant

3. Conservation of Angular Momentum Examples 1.The spinning volunteer.

5. Conservation of Angular Momentum Examples a. What is their angular speed after coupling?

6. Conservation of Angular Momentum Examples a. What is their angular speed after coupling?

7. Conservation of Angular Momentum Examples

8. 2.Two children, each with mass M, sit on opposite ends of a narrow board with length L and mass M. The board is pivoted at its center and is free to rotate in a horizontal circle without friction. (Treat the board as a thin rod.) a.What is the rotational inertia of the board plus the children about a vertical axis through the center of the board?

9. Conservation of Angular Momentum Examples 2.Two children, each with mass M, sit on opposite ends of a narrow board with length L and mass M. The board is pivoted at its center and is free to rotate in a horizontal circle without friction. (Treat the board as a thin rod.) b.What is the magnitude and direction of the angular momentum of the system if it is rotating with angular speed ω o in a clockwise direction as seen from above? Downward

10. Conservation of Angular Momentum Examples While the system is rotating, the children pull themselves toward the center of the board until they are half as far from the center as before. c.What is the ratio of the new rotational inertia to the initial rotational inertia?

11. Conservation of Angular Momentum Examples While the system is rotating, the children pull themselves toward the center of the board until they are half as far from the center as before. d.What is the resulting angular speed in terms of ω o ?

12. Conservation of Angular Momentum Examples While the system is rotating, the children pull themselves toward the center of the board until they are half as far from the center as before. e.What is the change in kinetic energy of the system as a result of the children changing their position? (From where does the added kinetic energy come?) The added energy comes from the work done by the children when pulling themselves forward. *Note: L = constant E k = increases