[jessriedel]

I think the radial scales on which galaxies are frisbee-like (i.e., the tangential velocity is roughly proportional to radius so that rotation period is constant) are much smaller than the scales on which we notice the discrepancy from naive expectations that suggests dark matter. The discrepancy in the velocity curve is at radiuses where both dark-matter and non-dark-matter models predict that velocity increases sub-linearly with radius. (It's true the dark-matter models are closer to linear than the non-dark-matter models, both are clearly distinct for it, and hence show whirlpool-like motion rather than frisbee-like motion). See the third figure here:

https://physics.stackexchange.com/questions/134159/what-is-a...