How to derive the gravitational potential on an infinitely thin disc of finite radius?

I am stuck on a problem that requires me to calculate the gravitational potential on an infinitely thin disc of finite radius $$R$$ with mass $$M$$. This infinitely thin disc models a galaxy. Once I have this potential, I am going to use it to calculate the angular velocity of a star within the disc. There is a constant density throughout the disc. I have seen analogous problems in electromagnetics, that calculate the potential on the edge of disc for a constant charge density, but they do not provide a formula for calculating the potential at any given point within the disc. Is there a better way to get the angular velocity? If not, how do I derive the potential on the disc?

• You can treat any mass distribution as an infinite collection of infinitesimal masses. Since you know the potential of a point mass, you can use superposition to obtain the potential of an arbitrary distribution as an integral. – G. Smith Apr 10 at 4:01