First, this is not a homework assignment even though it may seem like a homework type question. I have no problem with the derivation of the moment of inertia of a cylinder but am having more trouble with a sphere. I completely understand the often referenced disk method, but, I would like to take a shell method approach. THe following work is wrong conceptually, I think mathematically it is fine, and I hope someone can point me in the right direction. I dont see what one would need to do it using discs, and am assuming that some slight variation on the following should work: I=[tex]\int[/tex]r2dm p=dm/dv dvp=dm I=[tex]\int[/tex]r2pdv v=4/3[tex]\pi[/tex]r3 dv=4[tex]\pi[/tex]r2dr I=[tex]\int[/tex]r2p4[tex]\pi[/tex]r^2dr I=4[tex]\pi[/tex]p[tex]\int[/tex]r^4dr (Evluated between 0 and R) I=4[tex]\pi[/tex]pR5/5 p=m/v=m/(4/3 [tex]\pi[/tex] r3) Plugging that in and simplifying I get I=3/5mr2, though I need 2/5mr2. I think the problem lies in my set up, conceptually, and that I need to set up an equation somewhere subtracting two values (R from r?) though I am not sure. If you could help me out I would really appreciate it. And again, I understand and have no problem with the disk method for this, I am just trying to figure out what this method is not working. Thanks!