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Small mass element for laminar (moment of inertia)

  1. May 3, 2014 #1
    Hi, I was just going over the moment of inertia for a 2D lamina, Ive been happy with writing the small mass element dM as dM = ρdxdy where ρ is the area density, but for some reason decided on doing it like this,

    M(x,y) = ρxy


    dM = [itex]\frac{∂M}{∂x}[/itex]dx + [itex]\frac{∂M}{∂y}[/itex]dy
    = ρ(ydx + xdy)

    This is obviously not the same, and does not give the same answer when substituting in for dM in the moment of inertia tensor. I would like to know if there's a difference between the dM's, and if so why? Thanks.
  2. jcsd
  3. May 4, 2014 #2
    M(x,y) = ρxy

    This means the mass increases with increasing x and y which I don't think is what you want to model. But if it was then ρ is not constant and should be a function of x and y instead.
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