This is known as parallel axes theorem.
Statement:
If IG be the moment of inertia of a body of mass M about an axis passing through its centre of gravity, then MI (I) of the same body about a parallel axis at a distance 'a' from the previous axis will be given as I = IG + M a2
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the moment of inertia of a solid cylinder about an axis passing through its COM and parallel to its length is mr2/2 where r is the radius.
A rotating body that spins about an external or internal axis (either fixed or unfixed) increase the moment of inertia.
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(1/2) mr2, assuming the axis of rotation goes through the center, and along the axis of symmetry.
It is the square root of ratio moment of inertia of the given axis to its mass.