Cut a disc the size you want, mount it in your portable electric drill, clamp the drill in a vice or something to hold it upright.
Now the hard bit, and some experimenting will be needed:
Turn on the drill at slow speed, get a pencil and, starting as close to the centre as you can, while the disc is rotating, draw a straight line to the outside of the disc.
When you stop the drill, you should have something approaching a spiral that you can use as a guide for the black colour.
Ian