1. The problem statement, all variables and given/known data A system of particles, forming a sphere of uniform mass density [tex]\rho[/tex] and radius R, rotates around the axis of the sphere with angular velocity [tex]omega[/tex](t) calculate the energy of the system. 2. Relevant equations we were told to solve the problem with this integral: E = [tex]\int[/tex] [tex]\rho[/tex] v2 (r) d3r 3. The attempt at a solution I took [tex]\rho[/tex] = M/( 4/3 [tex]\pi[/tex] R3) v3 = r2 [tex]\omega[/tex]2 and d3 r = r^2 sin [tex]\theta[/tex] dr d[tex]\phi[/tex] d[tex]\theta[/tex] integrating from 0 to R for r, from 0 to pi for theta, and from 0 to 2 pi for phi, I got 3/5 M R^2 [tex]\omega[/tex]^2 I think the answer ought to be 1/5 MR^2 w^2, right? Thanks for the help.