If the ring is off-center when it hits the disk, the disk will still spin, but the moment of inertia will be affected.
The off-center location of the ring will cause the disk to be unbalanced, which will cause the moment of inertia to be lower than it would be if the ring were centered. This means that the disk will not spin as rapidly or as long as it would if the ring were centered.
This means that the rotational energy of the ring will not be distributed evenly and the result will be an unbalanced, or skewed, rotation. This will cause an inaccurate measurement of the moment of inertia, as the off-center ring will not be able to provide a true representation of the rotational energy.
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