Q. What would occur if a disk one light second in circumference were to spin at 60 RPM?
Answer:-
60 revolutions for each minute is one revolution per second.
1 light second means distance light travels in one second.
What this denotes that points on this hypothetical disk's perimeter would need to travel at the speed of light to satisfy your conditions. This can't take place for anything that has mass.
Bottom line a disk this size couldn't spin at this speed.