Moment of Inertia of Plate: Integration Proves 1/3ma^2+b^2

AI Thread Summary
The discussion focuses on deriving the moment of inertia of a plate about an axis perpendicular to the plate and passing through one corner, resulting in the formula 1/3 m(a² + b²). Participants emphasize using integration to express both r² and dm in terms of x and y. The approach involves setting up a double integral of ρr², where ρ is the density, and integrating first with respect to x and then y. The integration limits are defined from 0 to a for x and 0 to b for y. This method effectively demonstrates the calculation of the moment of inertia for the specified axis.
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Show by integration that the moment of inertia of the plate about an axis that is perpendicular to the plate and passes through one corner is \frac{1}{3}m(a^{2}+b^{2})

I'm not sure at all how to approach this problem. I know that the moment of inertia is \int r^{2}dm but how do I use that in this instance?

Any help is appreciated.
 
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Write up both r2 and dm in terms of x,y and integrate with respect to x and y.

ehild
 
Should I use two separate integrals, then add them together?
 
It is a double integral of ρr2=ρ(x2+y2).
First integrate both terms with respect to x from 0 to a, taking y as constant. Then integrate the result with respect to y from 0 to b.

ehild
 
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