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Angular velocity of two disks

  1. Jul 25, 2013 #1
    1. The problem statement, all variables and given/known data
    Two disks are rotating about an axis common to both. The first disk has moment of inertia I and angular velocity ω. The second disk has moment of inertia 2I and angular velocity [itex]\frac{ω}{2}[/itex]
    Both rotate in same direction
    If both disks are pushed into each other what is the angular velocity of the larger disk when both are rotating together?

    xa9TyS2.png

    3. The attempt at a solution
    I dont know how to solve this.
    I was thinking in [itex]I+2I = \frac{ω}{2} + ω[/itex] but that doesnt make sense.
    Any idea in how to start solving this?
     
  2. jcsd
  3. Jul 25, 2013 #2

    rude man

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    Conservation of angular momentum.
     
  4. Jul 26, 2013 #3
    [1/2 Iω^2]1 + [1/2 Iω^2]2 = 1/2 (I1 + I2)ωc^2
    Where ωc is the common angular velocity
     
  5. Jul 26, 2013 #4

    rude man

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    EDIT:
    this is not conservation of angular momentum. It's an energy equation which is invalid since heat is dissipated when the two disks conjoin.
     
    Last edited: Jul 26, 2013
  6. Jul 27, 2013 #5
    Oh my bad. That's a very specific case. Sorry.

    I1ω1 + I2ω2 = (I1 + I2)ωc
     
  7. Jul 27, 2013 #6

    rude man

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    That is correct.
     
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