The moment of inertia of a semicircular ring | vedclass

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Question

(A) complete circular ring of mass $M$ and radius $R$ has a moment of inertia $I = MR^2$ about an axis passing through its center and perpendicular to

Vedclass · Accepted Answer

$MR^2$

Vedclass · Answer

(A) complete circular ring of mass $M$ and radius $R$ has a moment of inertia $I = MR^2$ about an axis passing through its center and perpendicular to its plane.Since a semicircular ring is just half of a full ring,we can consider it as a system of particles where each particle is at a distance $R$ from the center.The moment of inertia is defined as $I = \sum m_i r_i^2$.For a semicircular ring,every mass element $dm$ is at a distance $R$ from the center.Therefore,$I = \int r^2 dm = \int R^2 dm = R^2 \int dm = MR^2$.Thus,the moment of inertia of a semicircular ring about an axis passing through its center and perpendicular to its plane is $MR^2$.

The moment of inertia of a semicircular ring of mass $M$ and radius $R$ about an axis passing through its center and perpendicular to its plane is:

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