EXAMPLE 4 Find the moments of inertia Ix, Iy, and I0 of a homogeneous disk D with density rho(x, y) = rho, center the origin, and radius a. SOLUTION The boundary of D is the circle x2 + y2 = a2 and in polar coordinates D is described by 0 ≤ θ ≤ 2π, 0 ≤ r ≤ a. Let's compute I0 first: I0 = D (x2 + y2)rho dA = rho 2π 0 a 0 r2 r dr dθ = rho 2π 0 dθ a 0 r3 dr