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Homework Help: Student on a Turntable

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data
    A student of mass m=40 kg is standing on the edge of a uniform, frictionless turntable, with diameter d = 5m and mass M=400 kg. The student and the turntable are initially rotating counterclockwise together about a fixed axis through the center of the turntable with an angular velocity of wi = 2 rev/min.
    The student now start to walk around the edge of the turntable so that the turntable comes to rest. What is the resulting speed v of the student relative to someone standing next to the turntable? In what direction is the student walking, clockwise or counter clockwise?

    2. Relevant equations
    conversion of rev/min to rad/s = rev/min * 1min/60s * 2(pi)/1rev
    Conservation of angular momentum:
    Li = Lf


    3. The attempt at a solution
    (Iturntable + Istudent)wi = Iturntable(wf) + Istudent(wfinal for student)
    ( (1/2)(400)(2.5)2 + (40)(2.5)2) (.209) = ( (1/2)(400)(2.5)2) (0) + ( (40)(2.5)2 ) wf

    Solve for wf and I got 1.254 rad/s
    Then use v = (r)wf = (2.5)(1.254) = 3.135 m/s
    The student is walking in the counterclockwise direction

    Can someone let me know if this is right? I thought it was too easy for a 30 point question
     
  2. jcsd
  3. Apr 27, 2010 #2

    kuruman

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    Gold Member

    I didn't plug in the numbers, but the method looks OK.
     
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