If rotation rate can be found by looking at shifts, what happens when mass is unevenly distributed?
Rotational rate is measured by looking at broadening of spectral lines, rather than shifting of spectral lines, since when an object is rotating, some parts are moving towards the observer and some parts are moving away. This causes a narrow spectral line to spread out. The particular shape of the broadened spectral line may change according to the distribution of mass in the object.