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.