Exploding Cylindrical Shell

A uniform cylindrical shell of mass $1$ is parametrized as follows:

$x = cos \theta \\ y = sin \theta \\ 0 \leq \theta \leq 2 \pi \\ 0 \leq z \leq 1$

The shell explodes, pulverizing the surface material and propelling the matter with the following initial velocity:

$\large{\vec{v_0} = (v_x, v_y, v_z) = (cos \theta, sin \theta, 0 )}$

After all of the matter has landed in the $xy$ plane, what is the moment of inertia of the debris field about the $z$ axis?

Details and Assumptions:
1) The matter stops immediately upon entering the $xy$ plane
2) Gravity is $10 \, \text{m/s}^2$ in the negative $z$ direction