Physics 2211 Mechanics Lecture 23 3D Rotation and Precession

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Physics 2211 - MechanicsLecture 233D Rotation
and Precession

• Dr. John Evans

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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.