Combination of translation and spinning, not rolling

AI Thread Summary
The discussion focuses on the dynamics of a spinning object that is also moving linearly, specifically in scenarios without friction or rolling. The user is exploring how linear motion affects the tangential velocities of points on the object's circumference, noting that the net tangential velocity consistently equals twice the center of mass velocity. This finding challenges the conventional understanding of rolling dynamics, suggesting that the relationship holds true even outside typical rolling scenarios. The user seeks mathematical resources to further understand this phenomenon. The conversation highlights the complexities of rotational dynamics in non-frictional contexts.
liometopum
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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?
 

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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.
 

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