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Homework Help: Angular Velocity again

  1. Nov 30, 2005 #1
    a cockroach of mass m lies on the rim of a uniform disk of mass 10m that can rotate freely about its center like a merry go round. Initially the cockroach and disk rotate together with an angular velocity of [tex] \omega_0[/tex]. Then the cockroach walks halfway to the center of the disk.

    What is the change in \Delta \omega[/tex] in the angular velocity of the system?

    I have no clue where to start...and no there are no numbers given.

    Can some one help me/give me a hint?
     
  2. jcsd
  3. Nov 30, 2005 #2
    You know that angular velocity = linear velocity v/r, the radius of the disk....
    The cockroach's initial angular velocity would have been some value like v/10 (Because the radius is 10m)
    I'm going to guess its angular velocity was the same when it was halfway through, in which case its angular velocity would be v/5...
    The difference would be v/5 - v/10 = 2v/10 - v/10 = v/10
    So the angular velocity would have gotten two times faster. (Assuming what I'm doing is right... which I'm unsure of)
     
  4. Nov 30, 2005 #3
    but the radius is not 10...
    mass of cockroach = m
    mass of disk = 10m (10 times as much as cockroach)
     
    Last edited: Nov 30, 2005
  5. Nov 30, 2005 #4

    mezarashi

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    Homework Helper

    When no numbers are given, assign variables and see if they cancel. You should apply the conservation of angular momentum principle

    [tex]I_1\omega_1 = I_2\omega_2[/tex]

    The intertial moment is due to the disk and cockaroach. The disk's moment remains the same in 1 and 2. The moment of inertia of a point mass is [tex]I = mr^2[/tex].
     
  6. Nov 30, 2005 #5
    so...how can I calculate everything if I dont have a radius?
     
  7. Nov 30, 2005 #6

    mezarashi

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    Homework Helper

    As I've said, assign variables. Let the radius be anything R. Now continue to solve.
     
  8. Jul 27, 2007 #7
    check the attached file

    << file with complete solution deleted by berkeman >>
     
    Last edited by a moderator: Jul 30, 2007
  9. Jul 30, 2007 #8

    berkeman

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    Staff: Mentor

    Thank you for trying to help, yellow_river. But we do not provide complete solutions to Homework Help questions here on the PF. Please be tutorial in your help.
     
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