- #1

- 194

- 0

## Homework Statement

Find the moment of inertia of a solid sphere of uniform mass density (like a billiard ball) about an axis through its center

## Homework Equations

I = ∫rρdV

## The Attempt at a Solution

I =ρ ∫r4πr

^{2}dr = ρ4π∫r

^{4}

Then I integrate this from 0 (the center) to R, so I = (ρ4π)*(R

^{5}/5)

And ρ = mv so ρ = M/(4/3)πR

^{3}= 3M/4πR

^{3}. Put ρ into the equation for moment of inertia to get I = 3MR

^{2}/5.

My book tells me the answer is (2/5)MR^2. Where did I go wrong?