A space station must spin in order to provide an artificial gravity for the occupants.  What is the gravity in the central non-spinning part of this ship? Zero.  If you went here, you'd be floating around freely.

If you were in a room on the outer edge of the rotating part, say 20m from the axis of rotation, what whould the linear velocity have to be in order to provide one g?
NOTE: "one g" means normal Earth surface gravity, 9.8m/s/s
Since a_c = v²/r,

9.8m/s/s = v²/20m

v = sqrt ( 9.8m/s/s * 20m) = 14m/s

What would that answer be in rad/s?
We know the circumference is 2pr, and we know that the velocity equals 2pr/T.  Doing it this way would give us m/s.
The arc length corresponding to one radian is 20m.
We need to get rid of the "m" and get to radians... to get rid of meters, we will multiply by the reciprocal of the radius...
14m/s * 1/20m = .7  What unit is this answer in?  Remember that radians are really dimensionless (no units), our answer here is in rad/sec.
Put more simply:  
 

NOTE: the "w" or angular velocity is called "omega"