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What is the moment of inertia of a disc about one of its diameter? |
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Answer» Solution :Suppose a DISC of mass M and RADIUS R in XY plane as shown in figure. Z is perpendicular axis to the plane PASSING through the centre of disc. Moment of inertia of disc about Z-axis `I_(Z)=(MR^(2))/(2)` ACCORDING to perpendicular axis theorem `I_(z)=I_(x)+I_(y)""....(1)` Since disc is symmetrical with axis x and y, `I_(x)=I_(y)` `therefore` From eqn. (1), `I_(z)=2I_(x)""........(2)` but `I_(z)=(MR^(2))/(2)` `(MR^(2))/(2)=2I_(x)` `therefore I_(x)=(MR^(2))/(4)andI_(x)=I_(y)` `therefore I_(y)=(MR^(2))/(4)` |
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