The diameter of each wheel of a bicycle is 26 inches. If you're traveling at a speed of 25 mph on this bicycle, through how many revolutions per minute are the wheels turning? So the first thing we're going to do is we're going to take this 25 mph and change it into inches per minute. Just by some straight conversions, we know that 5280 feet is the same thing as one mile. I put the mile in the denominator because I need the mile in the numerator and the mile in the denominator to cancel. We know that 12 inches is in one foot. I put the feet in the denominator so that it cancels with the feet in the numerator. So that's going to give me the inches that I'm going to need. So now I need to convert hours. I know one hour and 60 minutes. So the hour in the denominator, the hour in the numerator will cancel. So this gives me 26,400 inches per minute. Now angular velocity V is equal to R times Omega. If I wanted to solve for this Omega, you might think of it as AW we would have v / r Well our V is our velocity, so that's that. 26,400 inches per minute. We're going to divide by R, Or we could think of that as multiplying by 1 / R if R if the diameter is 26 inches, we know that the R is half that, or 13 inches, so one Radian per 13 inches. So angular velocity is in radians per minute in this case because the inches are going to cancel so 26,400 / 13 radians per minute. Now the last step here is going to be to convert the radians into revolutions and a full circle is 2π radians and a full circle is 1 revolution. So the radians are going to cancel and we would take 26,400, divide it by 13 and divide that by two Pi and we would get 323.2 revolutions per minute.