Given a uniform disc of mass M and radius R. A small disc of radius $$R/2$$ is cut from this disc in such a way that the distance between the centers of the two discs is $$R/2$$. Find the moment of inertia of the remaining disc about a diameter of the original disc perpendicular to the line connecting the centers of the two discs.

Question

Infinity Learn · Accepted Answer

Mass of cut disc: $$m1=M/4Moment$$ of inertia of original disc about axis $$1$$:$$I=14MR2Moment$$ of Inertia of small disc about axis $$1$$:I′$$=14m1R22+m1R22$$ or I′$$=516m1R2=564MR2$$ Required moment of inertia: I−I′$$=14MR2$$−$$564MR2=1164MR2$$

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