Paul, Bill S. has pretty much pointed it out, but I will go just one step further.
Assume an arc 1 foot from the origin that subtends 30 degrees. Now draw an arc 100 feet from the origin that subtends 30 degrees. I agree that the 100 foot arc will be much larger than the 1 foot arc. But they both are 30 degree arcs. If you move something along the 1 foot arc in 1 second its angular velocity will be 30 degrees per second. Now move something along the 100 foot arc in 1 second. Its angular velocity will be 30 degrees per second. Obviously the object on the 100 foot arc will be moving much faster than the one on the 1 foot arc, in order to move 30 degrees in 1 second. There is a large speed difference between 2 arcs. There will be no difference in the angular velocity.
Bill Gill
