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Would an object with high moment of inertia break if it is…

Would an object with high moment of inertia break if it is spun too fast?

If the reason for moment of inertia is because the mass furthest from the axis needes to cross longer distances in shorter time thus it needs high acceleration to keep up with mass thats closer to the axis, would an object break in extreme cases where high tension is developed between particles due to high moment? Assuming the object isnt strong enough to hold itself.
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