[godelski]

When I learned about dark matter I remember it being discussed about how the spin more like a solid rigid disk (ie: homogeneous mass distribution) vs a non-rigid (non-homogeneous) disk. That the distribution of visible matter did not predict the observed rotation behavior (moment of inertia problem, not center of mass. Though angular momentum is key).

An analogy for a non-rigid disk would be like swinging a flimsy plastic pipe. You'll notice that it is not straight when spinning and the far end lags the hand holding onto the rod. Vs if you spin with a metal pipe, the whole thing is rigid and your hand and the tip of the rod are in the same place.

The figure skater analogy is usually used in discussions about center of mass and moment of inertia (figure skater pulls arms in and the center of mass changes, but the energy is transferred into spin energy). Which rigid disks have a different moment of inertia than a non-rigid disk (eg: hoops spin different than disks).