Physics 121C Mechanics Lecture 23 3D Rotation and Precession December 6, 2004

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Physics 121C - MechanicsLecture 233D Rotation
and PrecessionDecember 6, 2004

• John G. Cramer
• Professor of Physics
• B451 PAB
• cramer_at_phys.washington.edu

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Course Evaluation

• Today we will start with a Physics 121C Course
  Evaluation, which will take 20 minutes. You are
  to rate the quality of the Lecture Part of
  Physics 121C only, using the distributed forms.
  Your participation is voluntary, and you may omit
  specific items if you wish. To insure
  confidentiality, do not write your name on the
  forms. Use ONLY A 2 PENCIL on the scannable
  forms. If you need a 2 pencil, raise your hand
  and one will be provided.
• There is a remote possibility that your
  handwriting on the yellow sheets could be
  recognizable. However, this should not be of
  concern. I will not see these results until
  after the quarter is over and you have received
  your grades.
• I have selected several monitors to distribute
  and collect the forms. They will place the
  completed forms and extras in an envelope and
  return it to the Office of Educational
  Assessment. I will leave the room and return in
  20 minutes, at 1055 AM, after the questionnaires
  have been completed and collected.
• Thanks for your participation!

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Lecture Schedule (Part 4)
You are here!
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Angular Momentumand Angular Velocity
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L as a VectorDemonstration Bike Wheel.

• I sit on the rotatable stool holding a bicycle
  wheel that is spinning in the horizontal plane.
  The rotation axis of the wheel is flipped by
  180o. The stool, with me on it, begins to rotate.
• Whats going on?

LW,f
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Turning the Bike Wheel

• Since there are no external torques acting on the
  person-stool system, angular momentum is
  conserved.
• Initially LINI LW,i
• Finally LFIN LW,f LS

LS
LW,I
LW,i LW,f LS
LW,F
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Clicker Question 1
I am initially at rest on the rotatable chair,
holding the wheel spinning as shown in 1. Now
2 I turn it over and the chair starts to
rotate. Question What happens if 3 the wheel
is turned over in the same direction one more
time?
??
1
2
3
(a) rotation stops (b) rotation doubles
(c) rotation stays the same
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Turning the BikeWheel Twice.
LNET
LNET
LNET
not turning
LW
LW
LS
LW
1
2
3
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Gyroscopic Motion

• Suppose you have a spinning gyroscope in the
  configuration shown below
• If the left support is removed,what will happen??

Support (to be removed)
pivot
?
g

• The gyroscope does not fall down!

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Reminder Circular Motion
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Gyroscopic Motion

• The gyroscope precesses around its pivot axis !
• This rather odd phenomenoncan be understood by
  usingthe vector character of

pivot
?
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Gyroscopic Motion

• The magnitude of the torque about the pivot is ?
  mgd.
• The direction of this torque at the instant shown
  is out of the page (using the right hand rule).
• The change in angular momentum at the instant
  shown must also be out of the page!

d
L
?
mg
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Gyroscopic Motion

• Consider a view looking down on the gyroscope.
• The magnitude of the change in angular momentum
  in a time dt is dL Ld?.
• Sowhere? ?df/dt is the precession frequency

L(t)
dL? d t
d?????????
pivot
L(tdt)
top view
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Gyroscopic Motion

• So
• In this example, ? mgd and L I?
• The direction of precession is given by applying
  the right hand rule to find the direction of ?
  and hence of dL/dt.

d
?
L
pivot
?
mg

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End of Lecture 23

• Before the next lecture, read sections 14.1
  through 14.6.
• The Final Exam will be held in this room on
  Monday, December 13 at 830 AM (Note NOT 1030
  AM!).
• Check Tycho for your seat assignment before
  coming to the Final Exam.
• Exam 3 should be graded and returned on
  Wednesday. Papers will be placed on the tables
  outside this room before and after Wednesdays
  lecture. Plan to come a bit early, if you can,
  and pick them up there.
• Exam 3 regrade requests will be accepted until
  noon on Friday, December 10.