Your Comments
The checkpoint problems about the spinning disk are slightly confusing to me still.
What material does the third exam cover?? Both this unit and applications?
i liked the prelecture and why is exam 3 soooo close :(
I was expecting this topic to be a bit challenging but it seemed quite simple.
These concepts are difficult... Please help us with examples during lectures!
This probably wont be on screen anyways but is there any other sites or places we
can go to read the material and maybe have some more practice problems? because
the homework isn't helping neither is the checkpoints.
The homework due for today was waaaay to long. Its bad enough I get 4 credit hours
for this class when I have to meet 6 hours a week throw over 2 hours of homework
on top of that and its just unreasonable. We do have other classes too.
I am very confused about the difference in the second and third checkpoint.
What would happen if the Earth SUDDENLY stopped spinning/ rotating?
Every week I give a shoutout commending the explanations of the one and only Gary
Gladding. Every week I never make the board. Poor Gary
how early do I have to enter this comment to get on the board?
not sure if people actually read this
Buckaroo Banzai was AMAZING! By the way if anybody wants another good laugh
check out "Flyin' Ryan" I believe the whole movie is on Youtube
Mechanics Lecture 19, Slide 1
Your grade so far
Prelectures + Checkpoints + Lectures
100
Labs
150
Hour exams (3 x 100 each)
300
Final Exam
200
Homework (14) + Quizzes (9)
250
Prelectures:
50
Preflight's:
25
Lecture participation: 25
You can miss up to 3 of each
For each Homework assignment, a score is assigned out of 100%
For each Quiz, a score is assigned out of 100%
The lowest of the 14 Homework and 9 Quiz scores is dropped.
The remaining scores are added together to give a number out of 2200.
This is scaled to be worth 250 points.
Bonus Points: You can earn up to 1 extra bonus point in every lecture (for a maximum of 25
bonus points for the semester) by getting the right answers to at least 5 of the clicker questions.
At the end of the semester your bonus points are added to your HW/Quiz score (max 250)
Your total score out of 1000 points determines your final grade.
Its just a simple formula – the computer calculates it.
Your grade is determined entirely by the your performance on
the components of the course as described above.
There is no other “extra credit” possible.
A+ (950), A (920), A- (900),
B+ (880), B (860), B- (835),
C+ (810), C (780), C- (750),
D+ (720), D (690), D- (610),
and F (<610).
Physics 211
Lecture 19
Today’s Concepts:
Angular Momentum
Mechanics Lecture 19, Slide 3
Linear and Rotation
Mechanics Lecture 19, Slide 4
Angular Momentum
We have shown that for a system of particles
Fext
Momentum is conserved if
dp

dt
Fext  0
What is the rotational version of this?
r
Well – to start with we know this:
 ext
  r F
L
d r  p
r  Fext 
dt
Mechanics Lecture 19, Slide 5
Torque & Angular Momentum
 EXT
 ext  r  FEXT
dL

dt
Lrp
In the absence of external torques
L  I
 EXT
dL

0
dt
Total angular momentum is conserved
Mechanics Lecture 19, Slide 6
Example – Disk dropped on Disk
top,initial  o
top, final  bottom, final   f
bottom,initial  0
“is friction between objetcs within a system an external force?”
No !!
Mechanics Lecture 19, Slide 7
Example – Disk dropped on Disk
top,initial  o
top, final  bottom, final   f
bottom,initial  0
1
Linitial  MR 2o  0
2
1
MR 2o  MR 2 f
2

1
1
2
L final  MR  f  MR 2 f
2
2
1
 f  0
2
Mechanics Lecture 19, Slide 8
What about Kinetic Energy?
top,initial  o
top, final  bottom, final   f
bottom,initial  0
2
1 2 L
K  I 
2
2I
K before
L2

2 I before
same
K after
L2

2 I after
x2
Mechanics Lecture 19, Slide 9
CheckPoint
In both cases shown below a solid disk of mass M, radius R, and initial
angular velocity o is dropped onto an initially stationary second disk
having the same radius. In Case 2 the mass of the bottom disk is twice
as big as in Case 1. If there are no external torques acting on either
system, in which case is the final kinetic energy of the system biggest?
A) Case 1
B) Case 2
C) Same
top,initial  o
top,initial  o
M
M
M
Same initial L
bottom,initial  0
bottom,initial  0
Case 1
Case 2
2M
Mechanics Lecture 19, Slide 10
CheckPoint
In which case is the final kinetic energy of the system biggest?
A) Case 1
B) Case 2
C) Same
M
2M
M
M
Case 1
A)The moment of inertia of case 2 is larger so the kinetic
energy would be smaller since L is the same in both
cases..
Case 2
L2
K
2I
B) more mass, more energy.
C) energy is conserved if no external torque. Both initial
energies were the same
Mechanics Lecture 19, Slide 11
Point Particle moving in a Straight Line
L  R p
axis

R1
1

p
  
L1  R1  p
 R1 p sin( 1 )
 pD

R2

R3
2

p

 
L2  R2  p
 R2 p sin( 2 )
 pD
D
3

p

 
L3  R3  p
 R3 p sin( 3 )
 pD
Mechanics Lecture 19, Slide 12
L  mvD  pD
L  R p
axis
D

p
Direction given by right hand rule
(out of the page in this case)
Mechanics Lecture 19, Slide 13
Playground Example
Before
After
M

Top
View
R
m
v
LBefore  mvR
LAfter
1
 I  ( MR 2  mR 2 )
2
Disk
LBefore  LAfter
Kid
v
1

R 1  M 2m 
Mechanics Lecture 19, Slide 14
CheckPoint
The magnitude of the angular momentum of a freely rotating
disk around its center is L. You toss a heavy block onto the disk
along the direction shown. Friction acts between the disk and the
block so that eventually the block is at rest on the disk and rotates
with it. What is the magnitude of the final angular momentum of
the disk-block system:
A) > L
B)  L
C) < L
Top View
Instead of a block, imagine it’s a kid hopping onto a merry go round
Mechanics Lecture 19, Slide 15
CheckPoint
What is the magnitude of the final angular momentum of the
disk-block system:
A) > L
B)  L
C) < L
Top View
A) the angular velocity remains the same but the mass increases. Thus,
angular momentum is greater than L.
B) L is conserved and since the block is thrown toward the
rotation axis it has no initial angular momentum.
C) There is friction between the disk and the block.
Mechanics Lecture 19, Slide 16
Clicker Question
The magnitude of the angular momentum of a freely rotating disk
around its center is L. You toss a heavy block onto the disk along the
direction shown. Friction acts between the disk and the block so that
eventually the block is at rest on the disk and rotates with it. Is the
total angular momentum of the disk-block system conserved during
this?
A) Yes
B) No
Top View
There are no external torques
The block skidding on the disk is an internal torque (within the system)
Mechanics Lecture 19, Slide 17
CheckPoint
The magnitude of the angular momentum of a freely rotating disk
around its center is L. You toss a heavy block onto the disk along the
direction shown. Friction acts between the disk and the block so that
eventually the block is at rest on the disk and rotates with it. What is
the magnitude of the final angular momentum of the disk-block
system:
A) > L
B)  L
C) < L
Top View
Instead of a block, imagine it’s a kid hopping onto a merry go round
Mechanics
Lecture19,
19,Slide
Slide 18
Mechanics
Lecture
CheckPoint
What is the magnitude of the final angular momentum of the
disk-block system:
A) > L
B)  L
C) < L
Top View
A) It will be more than the original because the block is
adding more angular momentum..
B) angular momentum is conserved.
C) The block starts with an angular momentum in the
opposite direction of the disk so the total is less than
just L
Mechanics Lecture 19, Slide 19
Clicker Question
A student holding a heavy ball sits on the outer edge a merry go
round which is initially rotating counterclockwise. Which way
should she throw the ball so that she stops the rotation?
A) To her left
B) To her right
C) Radially outward
C
A
B

top view: initial
final
Bender in Space
Mechanics Lecture 19, Slide 20
Clicker Question
A student is riding on the outside edge of a merry-go-round
rotating about a frictionless pivot. She holds a heavy ball at
rest in her hand. If she releases the ball, the angular
velocity of the merry-go-round will:
A) Increase
B) Decrease C) Stay the same
1
Mechanics Lecture 19, Slide 21
Homework
Mechanics Lecture 19, Slide 22
m2
Linitial  I disko
m1
0
I disk
1
 m1 R 2
2
Mechanics Lecture 19, Slide 23
m2
1
K initial  I disko2
2
m1
o
I disk
1
 m1 R 2
2
Mechanics Lecture 19, Slide 24
m2
m1
0
Linitial  I disk 0
f
L final  ( I disk  I rod ) f
L final  Linitial
Solve for f
1
m2 L2
12
1
 m1 R 2
2
I rod 
I disk
Mechanics Lecture 19, Slide 25
L final  Linitial
Mechanics Lecture 19, Slide 26
M
f
K final
1
 ( I disk  I rod ) 2f
2
Mechanics Lecture 19, Slide 27
Just like
Faverage
P

t
for linear momentum
M
f
 average
L

t
for angular momentum
Lrod  I rod ( f  0 )
Mechanics Lecture 19, Slide 28