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Mouse onto the edge of phonograph turntable

  1. Mar 4, 2012 #1
    1. The problem statement, all variables and given/known data
    [itex]m[/itex]mouse [itex]= 0.06kg[/itex]

    [itex]r = 0.3m[/itex]

    [itex]\omega = 0.05 rad / s[/itex]

    Suppose angular speed does not change.
    What is the work needed for the mouse to go to the center.

    2. Relevant equations

    [itex]I[/itex][itex]o[/itex][itex]\omega[/itex][itex]o[/itex] = [itex]I[/itex][itex]f[/itex][itex]\omega[/itex][itex]f[/itex]


    3. The attempt at a solution

    If [itex]\omega[/itex] doesn't change ,then how can I use the above equation.

    Since [itex]I[/itex] of mouse would be equal to [itex]mr^2[/itex] then [itex]\omega[/itex] would change. I am stuck here. Oh, and it's not a homework, it's a problem that I was stuck at some time ago. Thanks for any help
     
  2. jcsd
  3. Mar 4, 2012 #2

    Doc Al

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    Staff: Mentor

    You can't. If ω is fixed then angular momentum is not conserved.
     
  4. Mar 4, 2012 #3
    So in this case would the work be equal to: [itex]mr^2[/itex] ?
     
  5. Mar 4, 2012 #4

    Doc Al

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    Staff: Mentor

    That's an expression for rotational inertia, not work.

    Can you please state the full problem as it was given?
     
  6. Mar 5, 2012 #5
    A 60 gm mouse falls onto the outer edge of a phonograph turntable of radius 30 cm rotating at 33rev/min. How much work must it do to walk into the center post? Assume that the angular velocity of the turntable doesn't change.
     
  7. Mar 5, 2012 #6
    Seems like you just need to find out the centripetal force that the mouse feels and then you'll have the work. Though I could be wrong.
     
  8. Mar 5, 2012 #7

    tiny-tim

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    hi tonit! :smile:
    yes, work done is the integral of force "dot" displacement

    so, first, what is the force needed, as a function of r ? :wink:
     
  9. Mar 5, 2012 #8
    There is a centripetal acceleration associated with rotation at constant angular velocity, [itex] a_c = \omega^2 r [/itex]. So if my suspicions are correct, you can interpret that as a force that must be overcome, [itex] F_c = m \omega^2 r [/itex]
     
  10. Mar 5, 2012 #9
    thanks to all of you. now it is all clear :D
     
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