1. Instructor: Dr. Tatiana Erukhimova
Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lectures 34, 35, 36
Hw: Chapter 14 problems and exercises

3. Torque and Angular Momentum
Conservation of Angular Momentum

4. “Walk the Plank”

5. Map of Texas

6. Because

8. Because

9. Brady, TX

10. Skyhooks
The skyhook alone won’t balance on your finger, but when you put a belt on it, it does! This is all because adding the belt which curves under as it hangs actually moves the center of mass right under your finger!

11. Vector directed along velocity
The larger the momentum, the larger force you need to apply in order to change its magnitude or direction
Motion along the straight line: momentum

12. Rotational motion: angular momentum
Moment of inertia
Angular velocity
Vector along axis of rotation

13. Conservation of angular momentum: when radius decreases, rotation velocity goes up

15. Torque and Angular Momentum
Conservation of Angular Momentum

16. Pr. 1
A bullet of mass m is fired in the negative x direction with velocity of magnitude V0, starting at x = x0, y=b. (y remains constant) What is its angular momentum, with respect to the origin, as a function of x? Neglect gravity.
Pr. 2
A ball of mass m is dropped from rest from the point x = B, y=H. Find the torque produced by gravity about the origin as a function of time.

17. Problem 6 p.267
Consider a massless teeter-totter of length R, pivoted about its center. One kid of mass m2 sits on the right end and another of mass m1 sits on the left end. What is as a function of θ, the angle the board makes with horizontal?

18. Two men of equal mass are skating in a circle on a perfectly frictionless pond. They are each holding onto a rope of length R. What happens to the magnitude of momentum of each man if they both pull on the rope, “hand over hand”, and shorten the distance between them to R/2. (Assume the men again move in a circle and the magnitude of their momenta are equal).

19. An ant of mass m is standing at the center of a massless rod of length l. The rod is pivoted at one end so that it can rotate in a horizontal plane. The ant and the rod are given an initial angular velocity 0. If the ant crawls out towards the end of the rod so that his distance from the pivot is given by , find the angular velocity of the rod as a function of time, angular momentum, force exerted on the bug by the rod, torque about the origin.

20. Moment of Inertia
For symmetrical objects rotating about their axis of symmetry:

21. A man stands on a platform which is free to rotate on frictionless bearings. He has his arms extended with a huge mass m in each hand. If he is set into rotation with angular velocity 0 and then drops his hands to his sides, what happens to his angular velocity? (Assume that the man’s mass is negligible and that his arms have length R when extended and are R/4 from the center of his body when at his sides.)

22. Newton’s law of gravitation

23. Orbital motion
Conservation of Angular Momentum

24. A block of mass M is cemented to a circular platform at a distance b from its center. The platform can rotate, without friction, about a vertical axle through its center with a moment of inertia, Ip. If a bullet of mass m, moving horizontally with velocity of magnitude vB as shown, strikes and imbeds itself in the block, find the angular velocity of the platform after the collision. b vB
axle
top view

25. Have a great day!
Hw: Chapter 14 problems and exercises