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Department of Physics and Applied PhysicsPHYS.1410 Lecture 23 Danylov
Lecture 23
Chapter 12
Conservation of Angular Momentum
Physics I
Course website:http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsI
Department of Physics and Applied PhysicsPHYS.1410 Lecture 23 Danylov
Today we are going to discuss:
Chapter 12:
Rotational Newton’s 2nd Law (general form): Section 12.11 Conservation of Angular Momentum: Section 12.11
IN THIS CHAPTER, you will continue discussing rotational dynamics
Department of Physics and Applied PhysicsPHYS.1410 Lecture 23 Danylov
In the previous class ….
Department of Physics and Applied PhysicsPHYS.1410 Lecture 23 Danylov
Translational – vs- Rotational N. 2nd law
amF
dtpdF
I
Translational N.2nd law Rotational N.2nd law
dtLd
Department of Physics and Applied PhysicsPHYS.1410 Lecture 23 Danylov
Angular momentum (about the origin) of an object of mass m dropped from rest (cont.).
Example
(cont.)
Department of Physics and Applied PhysicsPHYS.1410 Lecture 23 Danylov
Conservation of Angular Momentum
dtLd
Angular momentum is an important concept because, under certain conditions, it is conserved.
If the net external torque on an object is zero, then the total angular momentum is conserved.
,0 extIf
constL
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.
0int ernal
extdtLd
0dtLdthen
, so
Department of Physics and Applied PhysicsPHYS.1410 Lecture 23 Danylov
Angular Momentum Conservation helps to solve many problems
I11 I22
IL For a rigid body21 LL
Launch: leg and hands are out to make I large
Flight: leg and hands are in to make large
Landing: leg and hands are out to “dump” large
1212 )( II
large1 I mallI s2
Example Figure Skater’s Jump
Angular Momentum stays constant throughout the whole jump
1 2
small-1 large-2
ConcepTest Figure SkaterA) the same
B) larger because she’s rotating faster
C) smaller because her rotational inertia is smaller
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. Comparedto her initial rotational kinetic energy, her rotational kinetic energy after she pulls in her arms must be:
KErot = I 2 = (I ) = L (used L = I ). Because L is conserved, larger means larger KErot.
12
12
12
12
The “extra” energy comes from the work she does on her arms.
Department of Physics and Applied PhysicsPHYS.1410 Lecture 23 Danylov
Example Bullet strikes cylinder edge
A bullet of mass m moving with velocity vstrikes and becomes embedded at the edge ofa cylinder of mass M and radius R. Thecylinder, initially at rest, begins to rotateabout its symmetry axis, which remains fixedin position. Assuming no frictional torque,what is the angular velocity of the cylinderafter this collision? Is kinetic energyconserved?
Department of Physics and Applied PhysicsPHYS.1410 Lecture 23 Danylov
Bicycle wheel/turntable as a demo of Angular Momentum Conservation
Department of Physics and Applied PhysicsPHYS.1410 Lecture 23 Danylov
Bicycle wheel/Ang. Mom. Conservation
xL
wzL
pzL
Initial situation Final situation
finz
inz LL
Angular Momentum Conservation (z comp):
pz
wz
finz LLL 0 w
zpz LL wwpp II
wp
wp I
I )( counterclockwiseclockwise
0inzL w - wheel
p - person
ConcepTest Spinning Bicycle WheelYou are holding a spinningbicycle wheel while standing on astationary turntable. If yousuddenly flip the wheel over sothat it is spinning in the oppositedirection, the turntable will:
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.
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
finz
inz LL
tablemeLLL zLL tableme 2
L
L2L
Department of Physics and Applied PhysicsPHYS.1410 Lecture 23 Danylov
Thank youSee you on Wednesday
