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Moment of inertia

  1. Nov 6, 2006 #1
    helllo, im having trouble finding the moment of inertia for a square uniform plate with length h on the sides...how do you go about it when the interia is about the x axis....the z axis is perpendicular to the square in this case... i understand how to do it when it is with respect to the z axis...the double intergral and all but when its on the xaxis i get confused...how do you set that up.
     
    Last edited: Nov 6, 2006
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  3. Nov 6, 2006 #2

    OlderDan

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    It should be easier to do it for the x axis than for the z axis. I assume the origin is in the center of the plate, with the x axis being a line that divides the plate into two equal rectangles. Consider a mass element dm = σdxdy and integrate x^2dm over the area of the plate. The y integral is very simple since there is no function of y in the integrand. You just get h, which is constant for all x. All that is left is the integral of x^2.
     
  4. Nov 6, 2006 #3
    Now when I integrate what do I integrate from 0 to h?
     
  5. Nov 6, 2006 #4

    OlderDan

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    If the axis is as I assumed, it is from -h/2 to +h/2. By symmetry, you could do twice the integral from 0 to h/2 and get the same result.
     
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