Due to its unusual shape I am unsure if the COG would be right in the center of closer to the side with (what looks like) more mass on the outside?
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If the centre of mass of any thin "slice" lies on the same circle centered in the origin and there is a uniform mass distribution, the center of gravity still lies in the origin. – Jack D'Aurizio Oct 02 '15 at 16:43
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Ok so then I would say it is not in the center since the slices would be radial from the center leading to uneven mass distribution. – Joe Oct 02 '15 at 16:51