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The moment of inertia of a disc about an axispassing through its centre and perpendicular toits plane is 20 kg m´2. Determine its moment ofinertia about an axiscoinciding with a tangent perpendicular to itsplane.passing through a point midway between thecentre and a point on the circumference,perpendicular to its plane. |
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Answer» Explanation: Inertia at center is 20kg−m ^2 Let, Mass of square PLATE, =m Side of square, =a inertia about perpendicular axis at center of square, I z=ma^2/6=20kg-m^2 Apply perpendicular axis THEOREM Iz= Ix+Iy=2Ix (square has same side) Ix=Iz/2=ma^2/12 Edge of square is at distance,a/2 from center Apply parallel axis theorem, I(edge)=Ix+m(a/2)^2 =ma^2/12+m(a/2)^2 =ma^3/3=2×ma^2/6=2Iz 2×20=40kg−m^2 40kg−m^2
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