A semicircular lamina of mass m has radius r and centre C. Its moment of inertia about an axis through its centre of mass and perpendicular to its plane is-

Question

G1 Physics · Accepted Answer

Use I=∫r²dm. For a shifted parallel axis use I=I about CM+Md²; for a plane lamina use I about z-axis=Iₓ+Iᵧ. Substituting the geometry/mass distribution given in the question gives (½-16/(9π²))mr².