belts and pullys

To do the calculation multiply your input speed by the diameter of the driver pulley then divide by the diameter of the driven pulley. In your case it would be the input speed times 9 divided by 8 to give the 12.5% speed up that C. Amick noted. For what it's worth the math works the same regardless of whether you have a speed up or slow down ratio.
 

The old guys figured the belt speed in feet/minute. If you know pi and can figure how far it is around each pulley it is easy to figure how fast a pulley will turn given a belt speed. If you have a pulley that is two feet around running at 100 rpm then the belt must be going at 200 ft/min. If you feed that to a pulley that is 1 ft around then that pulley will have to go at 200 rpm to take all the belt.
 

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