A uniform solid cylinder of length L and radius R has moment of inertia about its axis equal to I_ 1 . A small co-centric cylinder of length L / 2 and radius R / 3 carved from this cylinder has moment of inertia about

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For solid cylinder: I = (1)/(2)mR^2 Large cylinder: mass m_1 = π R^2 L , so I_1 = (1)/(2) π R^2 L × R^2 = ( π R^4 L)/(2) Small cylinder (carved out): length L/2, radius R/3, mass m_2 = π(R/3)^2(L/2) = ( π R^2 L)/(18) I_2 = (1)/(2) × ( π R^2 L)/(18) × (R/3)^2 = (1)/(2) × ( π R^2 L)/(18) × (R^2)/(9) = ( π R^4 L)/(324) (I_1)/(I_2) = ( π R^4 L/2)/( π R^4 L/324) = (324)/(2) = 162

A uniform solid cylinder of length L and radius R has moment of...

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