calculate the moment of inertia of a sphere of mass M and radius R by integrating over thin shells
The Attempt at a Solution
this is what i have so far
the sphere is decomposed into infinitesimal shells with surface area 4[tex]\pi[/tex]r2
the mass of each shell is dm=[tex]\rho[/tex](4[tex]\pi[/tex]r2)dr
after expanding rho and canceling terms I get
I=[tex]\int[/tex](2/3)(dm)r2dr from 0 to R.
I=2mrdr from 0 to R
this gives me I=mr2
does anyone see what I did wrong?
PS. those "pi" are not supposed to be powers. sorry, i'm not sure how to change them