Actually a galaxy's spin curve significantly diverges from a what we'd expect, like a "whirlpool" or say a solar system. It turns out stars on the rim do not complete orbits significantly slower than ones nearer to the center. It acts more like a frisbee. They're moving faster than they should but not getting "flung" out.

It is one of the reasons why dark matter was originally postulated; basically the galaxy system is much larger/massive than what we can see.

Adding a "Halo" of massive particles that are weakly interacting explains the curves fairly well--hence Dark Matter.