Guess what? I actually know what this is! VOR stands for "very high frequency omni-directional range" and is the system used by a series of stations around the world to help pilots figure how to get where they're going. This is, literally, how they get their bearings.
You may have seen some of these strange little stations off in the distance while driving out in the middle of no where. You can see a picture (and read a very brief explanation) here:
Each one sends out a signal. Pilots configure their equipment to head for these stations as they leapfrog across the country. I understand that, due to GPS, this system is becoming obsolete.
This wheel has four discs and is made of a very sturdy, heavy plastic. It's four and a quarter inches long along the longest point. Don't ask me how it works, though.