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Find the moment of inertia of a uniform ...

Find the moment of inertia of a uniform cylinder about an axis through its centre of mass and perpendicular to its base. Mass of the cylinder is M and radius is R.

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We assume the rotation axis to be transverse axis through the centre of mass of the linear molecule `H_2`. Then each of the hydrogen atom is a distance `1/2R` from the CM. Therefore, the MI of the molecule about this axis, `I=2m(R/2)^2=1/2mR^2`.
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