# A classical mechanics problem by Rocco Dalto

Let lamina $$S: x^2 + y^2 = 1, 0 \leq z \leq h$$, and axis $$A:$$ the line $$y = x, z = 0$$ .

If the moment of inertia $$I$$ of the lamina $$S$$ of unit density about $$A$$ can be expressed as $$I = \pi h \left (\dfrac{a}{b} h^2 + c\right)$$, where $$a$$, $$b$$, and $$c$$ are coprime positive integers, find: $$a + b + c$$.

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