[teamonkey]

It's a bit more abstract than that. The finding is actually that there's an approximately linear relationship between the measured distance of the outermost edge of a galaxy from its centre, and the average linear velocity of objects at that distance.

Define a rotating circle based on those two measurements, for each galaxy. These hypothetical circles will all have similar angular velocities no matter how big they are, hence they all take roughly the same amount of time to make one rotation.