Physics 101: Lecture 19 Rotational Dynamics

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Physics 101 Lecture 19Rotational Dynamics

• Todays lecture will cover Textbook Chapter 9
• Concept Questions and Example Problems
• More on Angular Momentum and Conservation of
  Angular Momentum

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Angular Momentum
See text chapters 8-9
Momentum Angular Momentum p m v L I
? conserved if ?Fext 0 conserved if ??ext
0 Vector Vector! units kg m/s units kg
m2/s
See Table 8.1
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Concept Question

• 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.

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Concept Question

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

This is like the spinning skater example in the
book. Since the net external torque is zero (the
movement of the arms and hands involve internal
torques), the angular momentum does not change.
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Concept Question

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

as with the skater example given in the
book....as you pull your arms in toward the
rotational axis, the moment of inertia decreases,
and the angular velocity increases.
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Concept question

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

Your angular velocity increases and moment of
inertia decreases, but angular velocity is
squared, so KE will increase with increasing
angular velocity
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Spinning disks

• Two different spinning disks have the same
  angular momentum, but disk 2 has a larger moment
  of inertia than disk 1.
• Which one has the biggest kinetic energy ?

(a) disk 1 (b) disk 2
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Preflights 7 8 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). She
  now turns the bike wheel over. What happens?
• 1. She starts to spin CCW.2. She starts to spin
  CW.3. Nothing

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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
• Finally LFIN LW,F LS

LS
LW,I
LW,I LW,F LS
LW,F