What diameter does a rotating space station have to be to generate useful gravity

[Cheap Astronomy]

Sorry - I meant to say space station in the title

First question - I've heard that to generate useful artificial gravity a rotating space station (like in the 2001 movie) one has to have a quite large diameter spin platform so that you can stand erect and conscious without your blood draining from your head to your feet. Are there some available metrics on this (i.e. what's the ideal diameter and spin velocity?)

Second question - if you ran really fast counter to the direction of spin, could you reverse the artificial gravitational effect?

Thanks, Steve