Find the moment of inertia of a solid sphere of uniform mass density (like a billiard ball) about an axis through its center
I = ∫rρdV
The Attempt at a Solution
I =ρ ∫r4πr2dr = ρ4π∫r4
Then I integrate this from 0 (the center) to R, so I = (ρ4π)*(R5/5)
And ρ = mv so ρ = M/(4/3)πR3 = 3M/4πR3. Put ρ into the equation for moment of inertia to get I = 3MR2/5.
My book tells me the answer is (2/5)MR^2. Where did I go wrong?