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Question

Seven identical circular planar disks, each of mass $$M$$ and radius $$R$$ are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point $$P$$ is?
1100240_5a00a72ad8074f4aac1fd97f13f1e58e.png


Solution

$$I_o={I}_{cm}+md^2$$

$$=\dfrac{7MR^2}{2}+6(M\times(2R)^2)$$

$$=\dfrac{55MR^2}{2}$$

$$I_p=I_o+md^2$$

$$=\dfrac{55MR^2}{2}+7M(3R)^2$$

$$=\dfrac{181}{2}MR^2$$


Physics

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