The moment of inertia of a uniform semicircular wire of mass M and radius r about a line perpendicular to the plane of the wire through the centre is ___________ .

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M r^2 Consider an element of length, dl = rd$\theta$. dm = M/$\pi$ rdl = M/$\pi$ rrd$\theta$ MOI of semicircular wire = \int_0^$\pi$ r^2 dm I = \int_0^$\pi$ r^2 m/$\pi$ rrd$\theta$ \Rightarrow I = m r^2 [Solution diagram: 67062_solution_1.png]

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