Lecture 23 Chapter 12 Physics I Conservation of Angular Momentum Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi
IN THIS CHAPTER, you will continue discussing rotational dynamics Today we are going to discuss: Chapter 12: Rotational Newton s 2 nd Law (general form): Section 12.11 Conservation of Angular Momentum: Section 12.11
In the previous class.
Translational vs- Rotational N. 2 nd law Translational N.2 nd law F F ma dp dt Rotational N.2 nd law I dl dt
Example Angular momentum (about the origin) of an object of mass m dropped from rest (cont.). (cont.)
dl dt Conservation of Angular Momentum Angular momentum is an important concept because, under certain conditions, it is conserved. In Ch11 we derived the linear momentum conservation, where we showed that internal forces cancel each other out and cannot change the total linear momentum. Similar, torques produced by the internal forces cancel each other out and cannot change the total angular momentum. So, only external torques are left to play the game. int ernal 0 dl dt ext ext 0, If the net external torque on an object is zero, then the total angular momentum is conserved. If L const then dl dt 0, so
Example Figure Skater s Jump Angular Momentum Conservation helps to solve many problems I1 large -small 1 I 2 2 small -large Angular Momentum stays constant throughout the whole jump Flight: leg and hands are in to make large 1 2 L 1 L 2 L I I 1 1 I 2 2 I I For a rigid body ( 2 1 2) 1 Launch: leg and hands are out to make I large Landing: leg and hands are out to dump large
ConcepTest A figure skater spins with her arms extended. When she pulls in her arms, she reduces her rotational inertia and spins faster so that her angular momentum is conserved. Compared to her initial rotational kinetic energy, her rotational kinetic energy after she pulls in her arms must be: Figure Skater A) the same B) larger because she s rotating faster C) smaller because her rotational inertia is smaller 12 111KE rot = 2I 2 = 2(I ) = 2 L (used L = I ). Because L is conserved, larger means larger KE rot. The extra energy comes from the work she does on her arms.
Example Bullet strikes cylinder edge A bullet of mass m moving with velocity v strikes and becomes embedded at the edge of a cylinder of mass M and radius R. The cylinder, initially at rest, begins to rotate about its symmetry axis, which remains fixed in position. Assuming no frictional torque, what is the angular velocity of the cylinder after this collision? Is kinetic energy conserved?
Bicycle wheel/turntable as a demo of Angular Momentum Conservation
Bicycle wheel/ang. Mom. Conservation Initial situation Final situation w L z L x in Lz 0 p L z w - wheel p - person Angular Momentum Conservation (z comp): in fin Lz Lz fin w p p w 0 Lz Lz Lz Lz Lz I p p I w w clockwise I w p ( )w I p counterclockwise
ConcepTest You are holding a spinning bicycle wheel while standing on a stationary turntable. If you suddenly flip the wheel over so that it is spinning in the opposite direction, the turntable will: Spinning Bicycle Wheel A) remain stationary B) start to spin in the same direction as before flipping C) start to spin in the same direction as after flipping L in z L fin z L L L me table L me table 2 L L z 2L The total angular momentum of the system is L upward, and it is conserved. So if the wheel has L downward, you and the table must have +2L upward. L
Thank you See you on Wednesday