Write an expression for the moment of inertia of annular disc of mass M about an axis passing through centre and perpendicular to plane of disc having:

(i) inner radii r₁ and outer radii r₂.

(ii) inner radii r and outer radii 2r.

Solution

left parenthesis straight i right parenthesis space Moment space of space Inertia space of space annular space disc space of mass space straight M space about space an space axis space passing space through space centre space and space perpendicular space to space the space plane space of space disc comma space space straight I equals 1 half straight M left parenthesis straight r subscript 2 superscript 2 plus straight r subscript 1 squared right parenthesis space left parenthesis ii right parenthesis space Moment space of space Inertia comma space space straight I equals 1 half straight M open square brackets open parentheses 2 straight r close parentheses squared plus left parenthesis straight r right parenthesis squared close square brackets equals 5 over 2 Mr squared

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