AZB Osmium Member
Why do you restrict the question with the word "now"?OK, you are just fucking with us now, right?
To clear up some errors or sources of misunderstanding above....
If a cue ball is on a bare slate slab, the area of the contact patch is significant. If the cue ball is spinning in place, like a top, the major source of friction is the boring friction of the contact patch. If that circular patch really has zero radius, there will be zero boring friction because no torque can be applied with a zero-length lever arm.
The area of the contact patch on a cloth-covered table can be estimated by how quickly a spinning ball stops spinning and knowing the coefficient of sliding friction. Both of those are fairly easy to measure. The problem is complicated because the weight of the ball is distributed over the patch in a non-uniform way, so you end up with a tricky integral to do and a couple of assumptions to make. Also, spinning in place probably changes the coefficient of sliding friction during the spin. I think the result from a simple analysis will probably give you the area within a factor of two or so.
The patch is larger with thicker cloth. That's easy to see in the difference in spin-down times for fuzzy snooker cloth and very thin carom cloth.