Prove that the expression where and represent, respectively, the moments and product of inertia of a given area with respect to two rectangular axes x′ and y′ through a given point O, is independent of the orientation of the x′ and y′ axes. Considering the particular case when the x′ and y′ axes correspond to the maximum value of show that the given expression represents the square of the tangent drawn from the origin of the coordinates to Mohr’s circle.
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