Having conceptual trouble with this aspect of centripetal force. Say we have a puck on a frictionless table attached to a string that I am holding through a small hole, so that the puck moves in a circular path. So $F=m\;\dfrac{v^{2}}{r}=m\;\omega^{2}\; r$. If I pull on the string to change the radius of the puck's path, does angular velocity change, or linear? The math makes it look like it could be either, or both, which seems like it can't be right.
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