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Short answer = 15 MPH on the outside edge of the wheel assuming no slippage. or about 174 RPM

Long answer:

For each unit of length that the bike moves forward, the outside edge of the wheel must travel the same distance, assuming no slippage.

For an RPM "speed":

Lets assume this is a road bike wheel, and that it happens to be a 29" diameter wheel.

That would mean the the circumference of the wheel is approximately 29" * 3.14 = 91"/12 = 7.6 feet

Assuming no slippage, for each inch of wheel circumference that travels around, you will move forward 1 inch.

So, each revolution of the wheel corresponds to 7.6 feet of forward travel.

A little bit of math gives us.

15 miles per 1 hour * 5280 feet per mile / 60 minutes per hour = 1320 feet per minute.

So if your moving across the ground at 1320 feet per minute, your wheel circumference must be moving the same 1320 feet per minute. We know that the circumference of the wheel is about 7.6 feet. So with 1320/7.6 = 174 we know the wheel must make 174 revolutions to make up the 1320 feet per minute.

So the wheel is spinning at 174 RPM.

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