I have no idea how to calculate that, so we'll just skip it. It's more than plenty enough to throw a baseball. I hate sewing, and I made a sling that can't fit anything larger than a baseball, so a baseball it is.
I wonder how you'd factor in the roller bearings when calculating arm inertia. I gather these things aren't usually built that way. The arm is ~2" wide along the pivot axis, but the contact patch is much narrower, since the only bearing surfaces are a couple of 1/4" thick roller bearings. Very low resistance; very smooooth. If I put a fixed weight on the bottom and give it a good shove, it will rock back and forth for 20 minutes.
I got to about 70' with half a brick. But your machine is much larger than mine. From ground to the top of the hook is 60".
Anyway, there are lots of trebuchets out there in the world that are bigger/stronger/faster/cooler than mine, but there's only one like this one, and I designed and built the thing myself, and it kicks ass, no matter what anybody else says. :)