# A classical mechanics problem by Tai Ching Kan

I have a uniform lamina of mass $$2m$$ in the shape of a regular hexagon, centre $$O$$ and vertices $$ABCDEF$$, clockwise in that order. I attach the following masses to the lamina: $$2m$$ at vertex $$C$$, $$m$$ at the midpoint of $$EF$$, and $$3m$$ at the midpoint of $$OB$$.

When I hang the lamina at $$A$$ so that it can rotate freely, find the angle that $$AB$$ makes with the downward vertical, giving your answer in degrees to 3 decimal places.

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