A math brainteaser for woodworkers?

[john patrick]

I would like to know the approximate RPM of my buffing wheels. The motor is rated at 1725 RPM. It has a two inch ID pully that drives a 3/4" ID" pully on the mandril. The buffing wheels are 6" diameter. So can anyone estimate how fast the buffing wheels are going when contacting the piece? And then, of course, the other question is: Is this an adequate speed for buffing?
Thanks!
John Patrick

[Jason Beam]

so you have a 2:.75 reduction of 1725 -- 2/.75 = 2.7ish, so 1725 * 2.7 = 4657ish RPM

The diameter of your wheel has no impact on RPM. It's the same RPM at 1" as it is at 50".

The SURFACE SPEED is impacted by the diameter, though. A 6" wheel has about 18.87" circumference - times 4657RPM you're looking at 87877.59 inches per minute, but it's more convenient to convert that to feet, so 87877.59 divided by 12 is 7323.1325 surface feet per minute.

as for whether it's adequate for buffing, i don't know.

[john patrick]

Since I see some folks buffing with direct drive systems on 3400 rpm motors, it looks like 4600 Rpm should be OK. Thanks for the help!
John Patrick

[Paul M Miller]

Here is a fun fact about calculating RPM and Pulley diameters. Most times you will know two things about one shaft, and one thing about the other shaft. If you multiply the two things you know on one shaft (RPM x Dia) and divide it by what you know about the other shaft (Dia) it will give you the unknown (RPM). Similarly, (RPM x Dia) of one shaft divided by the other shaft (RPM) will give you the unknown (Dia).

In your case, as Jason said: 1725 x 2.00 = 3450, divided by .75 = 4600.

Paul

[Jamie Cowan]

My head hurts.