Radian Measure with a ProRadian Protractor

This applet simulates an activity you can do with a radian scale protractor. Draw a line on a strip of paper and make a mark at one end. Place the zero of ProRadian 1 on the mark, and roll it along the strip. Every time an integer value "touches" the paper, make another mark on the strip. In the end, you'll have a "ruler" whose scale equals the radius of the protractor. Then roll ProRadian 2 along the same line, marking the sixths of π. You've just made a number line with both rational and irrational numbers on it. You can see how big those parts of π really are. ProRadian Protractors are available at www.proradian.net.
At approximately what value does it stop rolling? If it was a full circle, where would one full roll end?