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This is probably the stupidest question that I've come up with, and I'm a little embarrassed asking it, but here goes:

Is it only the tangential speed that is zero of a point at the axis of rotation in a rotating solid? If not, then I don't understand how the rotational speed of a point in a rotating solid exactly at the axis of rotation could be zero unless it is somehow detached from the rest of the whole solid. I mean solids behave all-in-one-piece right? So it has to be rotating with the rest of it?