Show that the moment of inertia of a spherical shell of radius

Show that the moment of inertia of a spherical shell of radius

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 ? is I = (8/15)p?R5. Then compute the change dI in I for a change dR, and use the fact that the mass of this shell is dm = 4pR2?dR.

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