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by wikipedia, the scalar moment of inertia for a solid body with continous mass-density function p, about a known axis can be calculated via:
where r maps x,y,z to the perpendicular distance from (x,y,z) to the axis of rotation and p maps x,y,z to the density of the solid at (x,y,z)
so in 2 dimensions, for a 2 dimensional solid, rather than a 3dimensional one you would have
now im trying to find this for a 2 dimensional rectangle.
if the rectangles centre is the axis of rotation, and the rectangle is centred on the origin with width = 2w, and height = 2h
then r would be:
if the mass-density is a constant m. then for all x,y
so i have:
evaluating the first integral
im pretty sure i must be getting something wrong along the way, because im fairly sure its not supposed to be 0 here.
Last edited by luca-deltodesco (2006-12-19 02:27:29)
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oh wait ofcourse i was adding it instead of taking it away
so i now have
anyone see any potential problems here?
Last edited by luca-deltodesco (2006-12-19 02:38:41)
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according to a physics textbook, it should be more like:
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no-one?
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Suppose you define W=2w, H=2h, and substitute w and h by W and H, the formula would be like the 3rd one.
X'(y-Xβ)=0
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W = 2w
H = 2h
yes, i guess it does, apart from having an extra WH in it
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