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Homework Help: Angular velocity and moment of inertia

  1. Apr 7, 2009 #1
    Could you let me know if my answers are correct?

    1. The problem statement, all variables and given/known data
    A light rope is wrapped several times around a large wheel with a radius of 0.400m. The wheel rotates in frictionless bearings about a stationary horizontal axis. The free end of the rope is tied to a suitcase with a mass of 0.15kg. The suitcase is released from rest at a height of 4.00m above the ground. The suitcase has a speed of 3.50 m/s when it reaches the ground.
    A) the angular velocity of the wheel when it reaches the ground and
    B) the moment of inertia of the wheel

    2. Relevant equations
    A) angular velocity (w) = speed/radius
    B) mgh = 1/2 mv2 + 1/2Iw2

    3. The attempt at a solution

    After using these equations I found angular velocity to be 8.75 rad/s and the moment of inertia to be 12.9 kg*m2.

    Correct or incorrect? Thanks for you help.
  2. jcsd
  3. Apr 7, 2009 #2


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    With ω = v/r then 8.75 looks ok.

    But your I looks a little large.

    m*g*h is total energy to start with dividing by ω2 where ω2 looks a lot bigger than m*g*h doesn't look right.
  4. Apr 7, 2009 #3
    Thanks for the reply. I also though I was rather large, but with my calculations that's what I ended up getting... strange.
  5. Apr 7, 2009 #4


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    I think you've done something wrong.

    Maybe show your numbers and how you got there.
  6. Apr 7, 2009 #5
    A) w = v/r = (3.50)/(0.400) = 8.75 rad/s

    B) Ki + Ui = Kf + Uf
    Ki and Uf = 0

    Ui = Kf
    mgh = 1/2 mv2 + 1/2Iw2
    (15)(9.8)(4) = 1/2 (15)(3.5)2 + 1/2 (I) (8.75)2
    588 = 91.9 + 38.3(I)
    496.1 = 38.3(I)
    I = 12.9 kgm2
  7. Apr 7, 2009 #6


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    Whoa. SI units please.

    m = .15kg
  8. Apr 7, 2009 #7
    Oh my gosh I can't believe I did that *facepalms*

    Thanks for your help, I really appreciate it
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