Hello friends,
It's been a while since I've been active on AZB, but thought I'd chime in for this one, just for fun.
From a visual observation of various slomo videos, the fastest instantaneous rotation I've seen on a cue ball (limited to my own shots) is around 1400 - 1700 RPM, about twice as fast as your idling car engine.
This is not a definitive statement at all - just an observation taken by visually judging the rate of rotation of a cue ball in a slomo video, then multiplying that by the "slow motion factor" of that particular slomo video. It's absolutely possible that other players can achieve higher (or lower) RPM.
To see some examples for yourself, you can look at my old videos and count the rotations to get a rough idea of the RPM as shown in the video (but do it quickly because it slows down surprisingly fast). If you have a musical background, you will get a feel for the "beats per minute" or speed of the cue ball rotation. Then simply multiply that by 8 or 14 or or whatever the factor is for the particular slomo clip you're watching.
All shots from 0:50 to 1:20 in the video link below were shot at 420 frames per second, and are now played back at 30 frames per second. That is a factor of 14. Conveniently, the main downbeats in the music are at 60 beats per minute (or 1 per second, duh!).
(Keep in mind that the rest of this video uses a combination of other speeds as well, so the "slomo factors" range from 4 to 33.)
So, if the cueball is completing one full revolution per musical downbeat, that would be 60 RPM x 14 = 840 RPM. In several of the shots, the cueball appears to approach two revolutions per musical downbeat, or about 1680 RPM. These aren't cold hard facts, just a quick visual/mental observation with a little math to convert units.
Use the music and the dots on the measle ball to help you judge the rotational speed. As you watch, your interpretation of the rotation may be a little different than mine.
Again, I didn't post this to settle any arguments. I just thought it'd be cool to be able to put an approximate number on some actual RPMs. Maybe it will come in handy as a reality check for whatever the math/physics equations come up with. Good luck with your research!
Here's the link. Judge for yourself. Have fun!
http://www.youtube.com/watch?v=dN5_NrkjQj8
-Blake