Physics 101: Lecture 16 Angular Momentum

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Physics 101 Lecture 16 Angular Momentum

• Todays lecture will cover Textbook Chapter
  8.7-8.9

• 1. Quiz this week Rotation, Rotational Inertia,
  Torque, Equilibrium
• 2. Prof. Ben Wandelt lecturing on Wednesday
• 3. Wont be in my office hours tomorrow. Avail
  Mar 18 or by appt.
• 4. Hour Exam II
• Monday, March 31
• Review session, 8pm, Mar 30
• Lectures 8-16
• Sign up online
• Special arrangements Alexey Bezryadin,
  bezryadi_at_uiuc.edu
• 5. Need a volunteer! (who does not get motion
  sickness)

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Suggested Practice Problems for Exam II
Chapter 5 Examples 5.3, 5.7, 5.8, 5.9, 5.11,
5.14 Problems 1, 5, 7, 14, 16, 39, 47, 74, 78,
88 Chapter 6 Examples 6.1, 6.2, 6.3,
6.6 Problems 6.1, 6.3, 6.13, 6.27, 6.31, 6.35,
6.37 Chapter 7 Examples 7.1, 7.3, 7.7, 7.8,
7.10, 7.11 Problems 7.1, 7.3, 7.5, 7.13, 7.15,
7.23, 7.21 Chapter 8 Examples 8.3, 8.5, 8.6,
8.7, 8.11, 8.13, 8.14Problems 8.3, 8.5, 8.9,
8.13, 8.23, 8.31, 8.33
Past hour exams http//online.physics.uiuc.edu/co
urses/phys101/spring08/practice/exam2.html
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Linear and Angular

• Linear Angular
• Displacement x q
• Velocity v w
• Acceleration a a
• Inertia m I
• KE ½ m v2 ½ I w2
• N2L Fma t Ia
• Momentum p mv L Iw

Today
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Define Angular Momentum
Momentum Angular Momentum p mv L
I? conserved if ?Fext 0 conserved if ??ext
0 Vector Vector! units kg-m/s units
kg-m2/s
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Right Hand Rule

• Wrap fingers of right hand around direction of
  rotation, thumb gives direction of angular
  momentum.
• What is direction of angular momentum for wheel
• A) Up B) Down C) Left D) Right

L Iw
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ACT Two Disks

• A disk of mass M and radius R rotates around the
  z axis with angular velocity ?i. A second
  identical disk, initially not rotating, is
  dropped on top of the first. There is friction
  between the disks, and eventually they rotate
  together with angular velocity ?f.
• A) wf wi B) wf ½ wi C) wf ¼ wi

Wheel rim drop
?i
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Act Two Disks

• First realize that there are no external torques
  acting on the two-disk system.
• Angular momentum will be conserved!

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Lecture 16, Pre-flights

• You are sitting on a freely rotating bar-stool
  with your arms stretched out and a heavy glass
  mug in each hand. Your friend gives you a twist
  and you start rotating around a vertical axis
  though the center of the stool. You can assume
  that the bearing the stool turns on is
  frictionless, and that there is no net external
  torque present once you have started spinning.
• You now pull your arms and hands (and mugs) close
  to your body.

stool demo
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Lecture 16, Preflight 1

• What happens to the angular momentum as you pull
  in your arms?
• 1. it increases 2. it decreases 3. it stays the
  same

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Lecture 16, Preflight 2

• What happens to your angular velocity as you pull
  in your arms?
• 1. it increases 2. it decreases 3. it stays the
  same

85 10 5
L Iw I 2mR2 I decreases, w increases
your angular momentum decreases because your
moment of inertia decreases when you pull in your
arms
Angular momentum is conserved when there is no
external torque acting on the system. ...
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Lecture 16, Preflight 3

• What happens to your kinetic energy as you pull
  in your arms?
• 1. it increases 2. it decreases 3. it stays the
  same

61 10 29
Angular momentum is conserved when there is no
external torque acting on the system. Angular
velocity and kinetic energy will increase when
your arms are pulled in because your mass is
closer to your rotational axis.
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What about Energy Conservation?

• A) Energy isnt conserved here
• B) Energy comes from weights
• C) Gravitational energy is being converted to
  rotational kinetic energy
• D) Energy comes from your breakfast

Did work not by creating a torque, t Did it by
changing I.
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Turning the bike wheel

• A student sits on a barstool holding a bike
  wheel. The wheel is initially spinning CCW in
  the horizontal plane (as viewed from above) L 25
  kg m2/s. He/she now turns the bike wheel over.
  What happens?
• A. She starts to spin CCW.B. She starts to spin
  CW.C. Nothing

wheel stool demo need volunteer!
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Turning the bike wheel...

• Since there is no net external torque acting on
  the student-stool system, angular momentum is
  conserved.
• Remenber, L has a direction as well as a
  magnitude!
• Initially LINI LW,I 25 kg m2/s
• Finally LFIN LW,F LS
• -25 kg m2/s
  Ls
• Ls 50 kg m2/s

LS
LW,I LW,F LS
LW,I
LW,F
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Turning the bike wheel (more)

• The student is holding the bike wheel and
  spinning counter clockwise. What happens if she
  turns it back again (so it is in the same
  orientation as it started).
• A) Spins Faster B) Stays same C) Stops

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Act 2 Rotations
A puck slides in a circular path on a horizontal
frictionless table. It is held at a constant
radius by a string threaded through a
frictionless hole at the center of the table. If
you pull on the string such that the radius
decreases by a factor of 2, by what factor does
the angular velocity of the puck increase?
(a) 2 (b) 4 (c) 8

puck on ice
w
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Act 2 Solution
Since the string is pulled through a hole at the
center of rotation, there is no torque Angular
momentum is conserved.
L Iw mR2w
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Gyroscopic Motion...

• L is a vector
• Suppose you have a spinning gyroscope in the
  configuration shown below
• If the left support is removed, what will happen?
• The gyroscope does not fall down!

bicycle wheel
pivot
?
g
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Gyroscopic Motion...

• Wheel starts to fall (slowly)
• Must keep vertical component of L zero
• Precesses around its pivot axis

pivot
?
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Summary

• St I a
• L I w
• Right Hand Rule gives direction
• If St 0, L is conserved