I just finished my tank tumbler- 1 year in the making! The business end was finished last year, but I added the motor this year because I was tired of using my bike to run it.
At any rate, I'm pretty good with math but was surprised that the numbers don't add up exactly right. I bought the pulley and shaft parts through McMaster, but a 10" pulley isn't quite 10" ID. I did make some estimates to account for the difference between ID and OD, but when gearing down, a small difference can have a pronounced effect.
I have a 3450 RPM motor and it was too slow although everything on paper said it should be just right. I was able to use the extra parts so that I could tumble 7" and 8" tanks and then "shift" gears and tumble smaller AL40s. I'm not sure if friction factors into this at all- I had some leftover parts and was able to make them work.
As far as the math goes, We start our thinking in terms of circumferences and rotations- a pulley that is 3" around will require 4 whole revolutions to turn a pulley that is 12" around. Lucky for us, circumference and diameter are proportional, so a 1" diameter pulley will require 4 whole rotations to turn a pulley that is 4" in diameter.
So going using a 1" pulley on your motor and connecting it to a 4" pulley will slow your RPMs down by 1/4. Lather, rinse, repeat, use bigger pulleys, and don't forget to consider the tank itself and the roller that drives it. You'll get the biggest reduction using a small pulley on the motor and large pulley on the drive shaft.
I have 3450 RPM motor. I used a 1-1/2" pulley on my motor, a 10" pulley and a 6" pulley on the jack shaft, and 10" pulley on the drive shaft with a 4L belt. The drive shaft has 2" rollers. It turns out to be roughly 75-80 RPMs for 8" and 7.25" tanks.
Based on your motor, you might be able use a 2" pulley on the motor and 10" pulley on the drive shaft (2" rollers, 8" tank, and everything else equal). Of course the beauty is in the details, unless you get one of those triple pulleys that have 3 circumferences on them so that you only have to get close
OK, I have a few more tanks to tumble...