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Parallel Axis Theorem problem help

  1. Dec 7, 2013 #1
    1. The problem statement, all variables and given/known data
    This is moreof a conceptual question regarding the parallel axis theorem and area.
    Lets say I have a solid rectangle with length L, and Width W.
    I cut out a circle of radius R at the center.
    When calculating the Total Area moment of inertia of the hollow region where the circle was cut out
    is it Itotal=Irectangle-(Icentral-Ad2) or
    Itotal=Irectangle-(Icentral+Ad2)
    because I know the region cut out has a negative area, so I subtract that moment of inertia from the rectangle's moment of inertia, but I'm not sure if that negative carries over inside the parenthesis as well

    2. Relevant equations
    Iany=Icentral + Ad2

    3. The attempt at a solution
     
  2. jcsd
  3. Dec 7, 2013 #2

    SteamKing

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    If you have a rectangle and then you remove a circular area from the center, the parallel axis theorem really doesn't come into play, because the centroid of the resulting figure hasn't changed from before the circular area was removed; i.e. I(net) = I(rectangle) - I(circle)
     
  4. Dec 7, 2013 #3
    I agree, but I wanted to explain what I was asking as simply as possible, the circle could be removed anywhere and it could be any series of shapes attached together. What I am confused on is if that negative area comes to play inside of the parenthesis or if it's |Ad^2|
     
  5. Dec 8, 2013 #4

    ehild

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    You cut out a positive area, that makes a negative contribution to the total moment of inertia.


    The second equation is correct.

    ehild
     
  6. Dec 8, 2013 #5
    thank you!!
     
  7. Dec 8, 2013 #6

    ehild

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    You are welcome:smile:

    ehild
     
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