Find the moment of inertia of a uniform semicircular disc of mass M and radius R about an axis perpendicular to its plane and passing through point P as shown.

Let the mass per unit length of the semicircular disc be M12πR2.Let us take a small strip of area πx dx, so mass of this strip is,   mass of the strip=M12πR2.πx dx.Therefore moment of inertia about the given point P,  I = M12πR2.πx dx. x2or                                    I = 2MR20Rx3 dx = 2MR2x440R=2MR2×R44=12MR2.

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