[NovemberWhiskey]

>GP has a point: consider the limiting case of an extremely long payload on an extremely short centrifuge arm. The payload is basically rotating around its own center of mass already, before release.

But isn't the payload rotating around its own center of mass because the centripetal force acting on the "front" of the payload is not parallel with the centripetal force acting on the "rear" of the payload? As soon as you cease to apply the centripetal force (i.e. release the projectile) you're no longer going to generate any torque.

Imagine the payload being held by ropes on the back and on the front and then both ropes releasing exactly as its center of mass passes through horizontal.