How do I assign a color ramp to a 360° axis? I know how to assign a color ramp to a single dimension (I.e. How to make a color gradient from red to white along the x axis)

What I am stuck with is how to make a color gradient based on a circular rotation.

For instance, if I had a circle, 0 would be red, PI/2 is yellow, PI is green, 3pi/2 is blue with the gradient working its way around.
You can set a Gradient Texture to Radial for this. Here i combined it with the Object Output of the Texture Coordinate Node, but depending on your geometry you might have to put a Mapping node behind it.