We can actually use the doppler effect on nearby stars to determine how fast they are rotating! The light from one half of the star is bluer than the other because part of the surface of the star is rotating towards us, and part away! Add up the difference in frequency (and do math), that tells you the difference in their speeds, half of that is how fast it's rotating! This is also handy when determining things like a star's absolute color and luminosity, as its spectrum can appear shifted or blurry if the star is rotating very fast or at a funny angle