What made me curious is that as the roll turns, the radius decreases, which lowers both the inertia and the torque that spins it. Do these balance out? I figured I'd try modelling what happens if you drop a roll while holding one end.
Since we're only interested in the roll rotating in the usual way, we can consider things in 2D:
where α is the angular acceleration of the roll. If we suppose each sheet has thickness T, we can relate the radius to the angle the roll has turned through: