Often, I find myself needing a wheel, plug, or round insert for something and don't have the round stock to make it. Here's the quick way I made a round cap to fit the winch in my small barn using a belt sander.
Step 1: Rough-Cut Your Circle
No real need for accuracy here. Just insure the shape you cut is larger than the diameter of the finished piece you want.
Step 2: Rough Sand Your Circle
Same goes for the initial sanding. Turn your piece smoothly enough to eliminate most flat spots. Check the diameter of your work often. Make sure you stay over your desired finished dimension in all directions. When you get close, stop sanding.