The moment of inertia of a uniform semicircul | vedclass

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Question

(C) For a complete circular disc of mass $M'$ and radius $r$,the moment of inertia about an axis perpendicular to its plane passing through the center

Vedclass · Accepted Answer

$M r^2$

Vedclass · Answer

(C) For a complete circular disc of mass $M'$ and radius $r$,the moment of inertia about an axis perpendicular to its plane passing through the center is $I = \frac{1}{2} M' r^2$.$A$ semicircular disc is exactly half of a complete circular disc.If the mass of the semicircular disc is $M$,then the mass of the corresponding full circular disc would be $2M$.Substituting $M' = 2M$ into the formula for the full disc:$I = \frac{1}{2} (2M) r^2 = M r^2$.Therefore,the moment of inertia of the semicircular disc about the axis perpendicular to its plane passing through the center is $M r^2$.

The moment of inertia of a uniform semicircular disc of mass $M$ and radius $r$ about an axis perpendicular to the plane of the disc passing through its center is:

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