A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R /2 is

Question

A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius $R /2$ is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.

TestHub · Accepted Answer

​ I complete ​ = 2 M R 2 ​ I removed ​ I = 2 M R 2 ​ ​ = ( 4 M ​ ) ( 2 R ​ ) 2 2 1 ​ + ( 4 M ​ ) ( 2 R ​ ) 2 = 32 3 M R 2 ​ − 32 3 M R 2 ​ = 32 13 ​ M R 2 ​ ​

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