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three diSc each of mass m and radius r placed in contact with each otheer find moment of inertia
Asked by devanshchauhan325 | 23 Dec, 2022, 07:34: AM
Figure shows the system of three discs each of radius R and mass M . Three discs are in contcat with each other as shown in figure.

Let us find the moment of inertia of this system about the axis passing through centre O . Let the axis be perpendicular to the plane of discs.

Centre of each disc is marked as A , B and C. Figure shows the equilateral triangle ABC formed by centres of each disc as vertices .

Distance from centre of system O to centre of each disc is (2/3) of median of triangle ABC .

OA = OB = OC = (2/3) ( √3 R )= ( 2 / √3 ) R

By parallel axis theorem , Moment of inertia I' of each disc is  [ (1/2) M R2 + M (2 / √3 )2 R2 ]

Hence moment of inertia of system I = 3 [ (1/2) M R2 + M (2 / √3 )2 R2 ]

Moment of inertia I = (  M R2 ) [ (3/2) + 4 ] = (11/2) M R2
Answered by Thiyagarajan K | 23 Dec, 2022, 08:43: AM

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