The angular velocity of a tire is 100 radians per second. The tire has a radius of 17 inches. How many revolutions does the tire make in 5 m

The radius doesn't matter....we're just concerned about the revs

2pi radians in one rev

So   in one second it makes     100   / [ 2pi ]   = ( 50 / pi )   revs

5 min  =   300 sec

So

300 (50 /pi)  =   15000  / pi   revs ≈   4774.6 revs