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Physics Problem on Angular Momentum

  1. Dec 5, 2011 #1
    1. The problem statement, all variables and given/known data

    A uniform 4.5 kg square solid wooden gate 1.5 m on each side hangs vertically from a frictionless pivot at the center of its upper edge. A 1.1 kg raven flying horizontally at 5.0 m/s flies into this gate at its center and bounces back at 2.0 m/s in the opposite direction. What is the angular speed of the gate just after it is struck by the unfortunate event.

    2. Relevant equations

    L=mvl and L=Iw


    3. The attempt at a solution

    First I calculated the momentum for the bird using L=mvl
    L = (1.1 kg)(5.0 m/s)(1.5m/2) = 4.125 kg m/s^2

    Then the total momentum after it strikes the square
    L(total) = raven + the square

    I wasn't sure about the moment of interia equation for the square so I used the one a thin rectangular plate axis along edge = Mr^2/3

    = (1.1kg)(-2.0 m/s)(1.5m/s) + (4.5 kg)(.75)^2/3(wf) = -1.65 kg m/s^2 + 0.84375(wf)

    I equated this to the intial momentum of the bird
    4.125 kg m/s^2 = = -1.65 kg m/s^2 + 0.84375(wf)

    wf = 6.8 rad/s which is way off

    Answer = 1.71 rad/s

    I think I'm having trouble as I can't visual the scenario properly...and help would be great!
     
  2. jcsd
  3. Dec 5, 2011 #2

    ehild

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    Homework Helper
    Gold Member

    Check the data in red.

    ehild
     
  4. Dec 5, 2011 #3

    gneill

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    Staff: Mentor

    The moment of inertia of a rectangular plate with dimensions a x b about its center, the axis being perpendicular to the sides of length b is

    [itex] \frac{1}{12} M \; b^2 [/itex]

    Note that the full length of the side, 'b' is used. Apply the parallel axis theorem to move the axis of rotation to the edge (along and 'a' side).
     
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