The moment of inertia of a uniform semicircul | vedclass

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Question

(C) full circular disc of mass $M_{total}$ and radius $r$ has a moment of inertia about an axis perpendicular to its plane passing through its center

Vedclass · Accepted Answer

$M r^2$

Vedclass · Answer

(C) full circular disc of mass $M_{total}$ and radius $r$ has a moment of inertia about an axis perpendicular to its plane passing through its center given by $I = \frac{1}{2} M_{total} r^2$.Since a semicircular disc is exactly half of a full circular disc,its mass is $M = \frac{M_{total}}{2}$,which implies $M_{total} = 2M$.Substituting this into the formula for the moment of inertia,we get:$I = \frac{1}{2} (2M) r^2 = M r^2$.Therefore,the moment of inertia of the semicircular disc about the specified axis is $M r^2$.

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

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