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Angular momentum of spinning mass on wheel

  1. Apr 25, 2013 #1
    1. The problem statement, all variables and given/known data

    An object of mass 2 kg is held in circular motion by a string of negligible mass.
    Initially the radius is 1 m and the tangential velocity is 4 m/s. The string is
    subsequently let out gradually until the radius doubles to 2 m. There are no
    frictional or resistive forces present. What is the final tangential velocity?


    2. Relevant equations
    v=wr
    L=Iw


    3. The attempt at a solution

    Initially the angular momentum is : 2*12*[itex]\frac{4}{1}[/itex] = L = 8

    By conservation of angular momentum we should have L = 8 when the string becomes 2m long :

    2*22*[itex]\frac{v^2}{2}[/itex] = 8 v=20.5

    Is this correct ?
     
  2. jcsd
  3. Apr 25, 2013 #2

    TSny

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    In your equation for the final angular momentum, you squared the velocity. Is that correct?
     
  4. Apr 25, 2013 #3
    Yes, is that a problem ?
     
  5. Apr 25, 2013 #4

    TSny

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    Did you square the velocity when finding the initial angular momentum? Why should it be squared in the final angular momentum?
     
  6. Apr 25, 2013 #5
    Ooops !!! I have absolutely no idea where that came in from. YIKES !

    So final tangential velocity is 2, correct ?
     
  7. Apr 25, 2013 #6

    TSny

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    Yes, that's the correct answer.
     
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