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Moments of inertia of a rectangular plate

  1. Jul 10, 2015 #1
    1. The problem statement, all variables and given/known data
    Show that the moment of inertia of a rectangular plate round it's diagonal, line B-B is equal to the one round a line parallel to one of the edges and passing through the center, line C-C

    2. Relevant equations
    Moment of inertia: ##I=mr^2##

    3. The attempt at a solution
    For the first case, round the diagonal: the MOI of a straight angle and isosceles triangle round one of the 2 identical edges is ##I=\frac{1}{6}ma^2##, and if i divide the plate into 4 such rectangles and calculate MOI it equals the one round line C-C.
    But is there an easier way?
     

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  3. Jul 10, 2015 #2

    Orodruin

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    Depending on your background knowledge, the symmetry of the square will tell you that they have to be equal.
     
  4. Jul 11, 2015 #3
    I have little background knowledge, please hint the subject that i have to study, is it principal axes? as far as i (think) i know i can't know anything about the MOI itself around principal axis, especially if they aren't orthogonal, but i am not sure.
    Please guide me to a book or publication that explains this topic, but, if possible, without the complexity of determinants, tensors etc.
     
    Last edited: Jul 11, 2015
  5. Jul 11, 2015 #4

    Orodruin

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    You can do it with principal axes, but all that is required is noting that an axis through the corners is a linear combination of the axes through the center and the center of the sides, which must have the same moment of inertia due to symmetry.
     
  6. Jul 11, 2015 #5
    So i just have to know the formula for modifying MOI with the changing of the angle of the axis?
     
  7. Jul 11, 2015 #6

    Orodruin

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    If you want to call it a formula, fine. The point is that any axis in the plane of the square has the same moment of inertia because the axes spanning the plane do.
     
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