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Angular momentum merry go round

  1. Dec 3, 2008 #1
    1. The problem statement, all variables and given/known data
    Suppose a 74 kg person stands at the edge of a 6.6 m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1820 kg.m^2. The turntable is at rest initially, but when the person begins running at a speed of 4.1 m/s (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction.
    Part A
    Calculate the magnitude of the angular velocity of the turntable.


    2. Relevant equations
    conservation of angular momentum


    3. The attempt at a solution
    this is how i approached it.
    initial angular momentum = 0
    final anglar momentum = I([tex]\omega[/tex]P) - I([tex]\omega[/tex]T)

    while [tex]\omega[/tex]p = v/r and IP = MR2

    MR2V/R - I([tex]\omega[/tex]T) = 0

    [tex]\omega[/tex]T = MRV/IT

    [tex]\omega[/tex]T = (74)(3.3)(4.1)/ 1820

    [tex]\omega[/tex]T = 0.55 RAD/S

    but due to some reason turns out to be the wrong answer , someone plz help ??
     
  2. jcsd
  3. Dec 3, 2008 #2

    Doc Al

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    Staff: Mentor

    The speed of the person is given with respect to the turntable, not with respect to the ground (which is what you need).

    Hint: If the angular speed of the turntable (with respect to the ground) is ω, what would be the angular speed of the runner with respect to the ground?
     
  4. Dec 3, 2008 #3
    what i think is that angular velocity of the person with respect to ground = 4.1 + angular velocity of table
    can be wrong though...someone reply as soon as possible this question is due within an hour
     
  5. Dec 3, 2008 #4

    Doc Al

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    Staff: Mentor

    Almost. But 4.1 m/s is a linear speed, not an angular velocity. Convert it to an angular velocity first.
     
  6. Dec 3, 2008 #5
    but what would be the angular velocity of the turntable then for finding the angular velocity of the person with respect to ground . do i use then one i calculated at my first attempt . and then plug it in to equation for finding the angular velocity of person with respect to ground.??

    and then after finding the angular velocity of the person with respect to ground u plug it back into the very first equation for finding angular velocity of the table.
    tried this whole thing but never worked.

    help ??
     
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