The discussion centers on the concept of angular velocity in the context of a rotating disc, specifically examining the angular velocity at the center of the disc and its implications for linear (or tangential) velocity. The scope includes theoretical considerations and potential implications of different physical scenarios.
Participants express differing views on the terminology and implications of linear versus tangential velocity, and the discussion remains unresolved regarding the implications of very small position vectors and non-classical cases.
The discussion does not resolve the definitions of linear and tangential velocity in the context of very small position vectors, nor does it clarify the implications of non-classical scenarios.
If ##\vec \omega## is constant, as I assume to be the case here, "tangential" and "linear" velocity are the same. When ##\vec{r}## is not zero but very, very small, then the linear velocity classically is not zero but very, very small.Seth Greenberg said:By 'linear velocity' you mean tangential velocity? What happens if ##\vec{r}## is not zero but very, very small, say the plank length?