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Show that the moment of inertia of a spherical shell of radius R and mass m is 2mR²/3. This can be done by direct integration or, more easily, by finding the increase in the moment of inertia of a solid sphere when its radius changes. To do this, first show that the moment of inertia of a solid sphere of density ρ is I=(8/15)πρR⁵. Then compute the change dI in I for a change dR, and use the fact that the mass of this shell is dm = 4πR²ρdR.

What I did is using I = ∫r²dm=∫4πr⁴ρdr=4πρR⁵/5=3MR²/5.

what is wrong with my equation? And please note that I am not asked to ask moment of inertia about the diameter.

Thanks ~

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# Moment of inertia about center of solid sphere

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