Combination of translation and spinning, not rolling

[liometopum]

All the texts and sites I can find discuss the rotational dynamics of pure rotation, pure translation, or a combination of an object rolling without slipping. I am trying to resolve some rotational dynamics regarding a spinning object that is moving linearly.. such as a planet in space or a tiny particle. No friction, not rolling. Sort of slipping without friction loss.

I have a diagram attached. The blue arrows represent the linear motion of the center of mass. The linear velocity adds to or subtracts from the tangential velocities of the points on the circumference.

Does anyone have a good source for the math of this option?

 

[liometopum]

In working on this, I just found that the net tangential velocity is always 2 times the velocity of the center of mass, regardless of translational velocity. I'd thought rolling was a special case, but surprise... the tangential velocities net out to 2 * velocity of the center of mass.