# Rotating ring with “thing” moving on it Say I have a ring with the center of mass G. Also I rotate the ring around a point P on the ring, and I have a "anything" moving along the ring at the same time with velocity v.

How would one explain the motion of the "anything"? Would one say that it's absolute velocity is the velocity of G + the relative velocity (velocity measured from P) + the rotational velocity of the entire system? Or is some of these terms zero?

Thank you.

• This seems like an interesting question, but could you clarify a bit? Does the main ring spin in its own plane, like spinning a hoola hoop around your waist, or does it spin about an axis in its own plane, like spinning a coin on its side on a table? Is there perhaps an existing object that behaves like this that you can give as an example? – ChP Apr 5 '18 at 11:03
• One way to describe it would be to define two separate rotation matrices for the "ring" and the "thing" and crossing the two and apply it to the "thing" – ChP Apr 5 '18 at 11:08
• A sketch or diagram would help clarify the question. – Daniel K Apr 5 '18 at 11:42
• I have added a picture. – 123 Apr 5 '18 at 14:48

$$x= \sqrt{1-y^2}$$ But G is turning with its $$X_p = \sqrt{1-Y^2_p}$$