SOLUTION: This is the word problem I am having issues with. If a bike with a 26 inch diameter wheel is traveling at 16 mph, then what is the angular velocity of the valve stem in radians

Every time the wheel turns through a complete revolution, it rolls through a
distance equal to its circumference.  

Since   the circumference is  which is about 81.7
inches.   I mile is 5280x12 or 63360 inches, and 16 miles (that it goes in an
hour) is 63360x16 or 1013760 inches. So we divide 1013760 by the circumference
and that tells us how many times the wheel turned during the time it travels 16
miles during that hour.  So it turned  or 12411.14732
rotations per hour.  Each rotation is  radians so we multiply:



 radians per hour.

Edwin