This trick works well for plastic discs. It automatifally finds dead centre and lets you cut any diameter within reason.
Glue the material to a sacrificial block that has been faced in the lathe's chuck (spray adhesive works well).
If a centre is required drill it first.
Measure your radius and mark several places with a pencil.
Turn on the machine and mark the ghost images you see spinning with the pencil.
Upturn a #11 X-Acto knife and cut the circle.
Note: For larger circles, sandwich the material between two pieces of wood and turn a diameter with conventional tools. The resulting disk will have perfect, clean edges. This sandwiching technique works well for non-ferrous metals as well.
John