This isn't a homework question or anything. Actually, it's a math related question that I've had to think about in the implementation of a physics program I'm perpentually trying to get to work in a realistic manner.

Now, I already know the 'correct' answer, but it took me a couple of days before I was like "oh, DUH" and then I kicked my cat*.

I'll post the correct answer if nobody can get it.

So here's the scenario:

A sphere (mathematically perfect sphere) is moving across a plane (a mathematically perfect horizontal plane). Lets just say we know the force of friction at any instant (the actual numbers don't matter), we know its linear and angular velocity at any instant, etc. How long does it take for the sphere to lose all of its kinetic energy (comes to a complete stop)?

I'm hoping that there aren't going to be any smart asses that are going to have an answer in like five minutes after I hit 'submit', in fact I'm kind of hoping you guys won't know otherwise I'm just kind of going to feel stupid.

* i didn't REALLY kick my cat, but i wanted to