Ellipticals supported by random motions As opposed to spiral galaxies, which are rotationally supported, elliptical galaxies are said to be supported by random motions of their stars. I don't really have an intuitive understanding of this. How do random motions prevent a collapse?
The same way rotation does.  If you look at each star, it is following some kind of orbit, so it has a motion.  The only difference between a spiral and an elliptical is that the motions in a spiral are all in the same plane and the same direction, but in the elliptical, they are all over the place.  So "random velocity" just means you look at a bunch of stars-- each one is still in an orbit, so it's no surprise it stays in orbit.