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The angular speed of the turntable with a woman on it? Help

  1. Nov 19, 2012 #1
    The angular speed of the turntable with a woman on it? Help!!

    Number18.png

    Ok so I understand part a (why it's counterclockwise. τ = Fr = (mg)(2) = (70)(9.8)(2) = +1372)

    Part b is where I'm stuck...
    This is what I did...

    PEinitial + [STRIKE]KEinitial rotational[/STRIKE] = [STRIKE]PEfinal[/STRIKE] + KEfinal rotational
    PEinitial = KEfinal rotational
    mgh = (1/2)Iω2
    (70)(9.8)(2) = (1/2)(5402
    1372 = 270ω2
    1372/270 = ω2
    5.08 = ω2
    2.25 rev/s = ω

    Convert to rad/s

    2.25/2π rad/s = 0.358 rad/s, but the answer is 0.389.
    Help! :( Where did I go wrong?
     
  2. jcsd
  3. Nov 19, 2012 #2
    Re: The angular speed of the turntable with a woman on it? Help!!

    Did the woman change her position in the VERTICAL direction?
     
  4. Nov 19, 2012 #3
    Re: The angular speed of the turntable with a woman on it? Help!!

    Brb in 2 hours!!
    In the meantime can someone answer my question?
     
  5. Nov 19, 2012 #4
    Re: The angular speed of the turntable with a woman on it? Help!!

    No/yes?

    Hold on! I have to go to class real quick!
    brb!
     
  6. Nov 19, 2012 #5
    Re: The angular speed of the turntable with a woman on it? Help!!

    Is angular momentum conserved here?
     
  7. Nov 19, 2012 #6
    Re: The angular speed of the turntable with a woman on it? Help!!

    If the OP is to learn anything then the OP must try to answer the question posted above, i.e. whether the woman changed her position in the vertical direction.
     
  8. Nov 19, 2012 #7
    Re: The angular speed of the turntable with a woman on it? Help!!

    Yes! She maintains a constant speed of 1.50 m/s, so the round table keeps turning (conservation of angular momentum)

    L = Iω
     
    Last edited: Nov 19, 2012
  9. Nov 19, 2012 #8
    Re: The angular speed of the turntable with a woman on it? Help!!

    Wait what?
     
  10. Nov 19, 2012 #9
    Re: The angular speed of the turntable with a woman on it? Help!!

    The woman is walking on a surface that stays horizontal. You've misunderstood the question.
     
  11. Nov 19, 2012 #10
    Re: The angular speed of the turntable with a woman on it? Help!!

    Wait are you talking to me?
     
  12. Nov 19, 2012 #11
    Re: The angular speed of the turntable with a woman on it? Help!!

    The total angular momentum of the entire system is conserved regardless of constancy of her speed. This is because there are no external forces acting on the system. How could you use this fact?
     
  13. Nov 19, 2012 #12
    Re: The angular speed of the turntable with a woman on it? Help!!

    1) Conservation of angular momentum (NO EXTERNAL FORCES acting on the system)

    Linitial = Lfinal
    [STRIKE](Ltable + Lwoman)initial[/STRIKE] = (Ltable + Lwoman)final
    0 = (Ltable + Lwoman)final
    0 = I1ω1 + I2ω2
    -I1ω1 = I2ω2
    ω1 = -(I2ω2)/I1

    2) Moment of Inertia for the woman (I2)

    I2 = mr2
    I2 = (70)(22)
    I2 = 280

    3) Angular Speed of the woman (ω2)

    ω = v/r
    ω = (1.50)/(2)
    ω = 0.75 rad/s

    4) Moment of Inertia for the table (I1) - this is given

    I1 = 540

    5) Plug and chug

    ω1 = -(I2ω2)/I1
    ω1 = -[(-280)(0.75)]/540
    ω1 = 0.389 rad/s
     
  14. Nov 19, 2012 #13
    Re: The angular speed of the turntable with a woman on it? Help!!

    Merci!
     
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