Your Comments
m1
m2
i studied so hard for exam 2... and i did so bad :'( why physics u no love me.
When we say a system will conserve angular momentum, does the solar system
count? Say the sun suddenly expands in volume when it nears its death, then it should
slow down its rotation, but will the planets also change rotational speed? Or if Uranus
shrinks, will Neptune speed up?
I never really liked this topic in high school. In fact I really hated it and didn't really
understand it. Hopefully it'll be different in college and in lecture because that seems
to be the trend.
The merry-go-round derivation was very difficult to follow... BUT, did you know that
the merry-go-rounds are now banned from school playgrounds because young
children have been severely hurt from increasing their omegas too much and then
flying off? A kid almost died doing this at my elementary school, then a huge
machine/crane thingy uprooted the merry-go-around.
Can we go over the "Block on Spinning Disk 2a"? I have a feeling that the total angular
momentum may be equal to the initial angular momentum of the disk, but I don't
know
could you go over the spinning disks
More examples in class would be helpful.
Were you a good student before you became a professor?
Mechanics Lecture 19, Slide 1
What was the average for the exam and is there a curve. I know some
people who did really well and some that didn't. I was among the ones that
didn't do as well, but I left the exam feeling very confident. I thought I
knew what I was doing- but I guess I don't. I go to office hours, do all the
practice exams and I feel like I understand the material. What else should
I be doing to do well on the exams?
Average: 75.4%
(no curve)
Mechanics Lecture 19, Slide 2
Your grade so far
Prelectures + Checkpoints + Lectures
100
Labs (9)
150
Quizzes (9)
100
Homework (26)
150
Hour exams (3 x 100 each)
300
Final Exam
200
Prelectures:
50
Preflight's:
25
Lecture participation: 25
You can miss up to 3 of each
The lowest Quiz is dropped
The lowest Homework is dropped
To get lecture participation credit you need to vote on at least half of the questions in a lecture.
(i.e. it is possible to get part of a bonus point but no participation point for a lecture)
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 scores (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).
Is there a way we can check our physics grade in the class as a
whole? I know I could calculate it from the grade book, but
that would take a lot of averaging, weighting, and dropping of
lowest scores, and I'd much rather spend all my free time
studying physics!
Yes – I made a spreadsheet for this yesterday.
I will post it someplace (use at your own risk)
Physics 211
Lecture 19
Today’s Concepts:
Angular Momentum
Mechanics Lecture 19, Slide 6
Linear and Rotation
Mechanics Lecture 19, Slide 7
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 8
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 9
Example – Disk dropped on Disk
top,initial  o
top, final  bottom, final   f
bottom,initial  0
Mechanics Lecture 19, Slide 10
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 11
What about Kinetic Energy?
top,initial  o
top, final  bottom, final   f
bottom,initial  0
2
1 2 L
K  I 
2
2I
Kbefore
L2

2 I before
same
K after
L2

2 I after
x2
Mechanics Lecture 19, Slide 12
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 13
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) K=L/2I, in case 1 the system has the smaller I
Case 2
L2
K
2I
B) …if two objects have the same velocity, the one with
greater mass will have greater kinetic energy…
C) Kinetic energy is the same because they start and
end with the same L
Mechanics Lecture 19, Slide 14
Point Particle moving in a Straight Line
L  R p
axis

R1
1

p
  
L1  R1  p
 R1 p sin(1 )
 pD

R3

R2
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 15
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 16
Playground Example
Before
After
M

Top
View
R
m
v
LBefore  mvR
LAfter
1
 I  ( MR 2  mR2 )
2
Disk
LBefore  LAfter
Kid
v
1

R 1  M 2m 
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 Lecture 19, Slide 18
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 moment of Inertia of the system is bigger than the moment of
Inertia of the disk.
B) Since the block is tossed horizontally towards the middle
of the disk, it doesn't add and momentum to the disk so the
momentum of the disk before must be equal to that of the
disk after.
C) There is friction so it will be less
Recycling answers doesn’t help you
Mechanics Lecture 19, Slide 19
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 20
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 21
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) the block in this case has an initial angular momentum..
B) Nothing really changed from 1a
C) The block has an initial angular momentum which
runs counter to the disk's angular momentum
“I don't understand how a change in direction of throwing the block onto the disk
causes L to not be conserved..how does the change in direction count as an outside
force?”
Mechanics Lecture 19, Slide 22
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 23
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 24
Homework
Mechanics Lecture 19, Slide 25
m2
Linitial  I disko
m1
0
I disk
1
2
 m1R
2
Mechanics Lecture 19, Slide 26
m2
1
K initial  I disko2
2
m1
o
I disk
1
2
 m1R
2
Mechanics Lecture 19, Slide 27
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
 m1R 2
2
I rod 
I disk
Mechanics Lecture 19, Slide 28
L final  Linitial
Mechanics Lecture 19, Slide 29
M
f
K final
1
 ( I disk  I rod ) 2f
2
Mechanics Lecture 19, Slide 30
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 31