Bicycle Wheels The diameter of each wheel of a bicycle is
26 inches. If you are traveling at a speed of 35 miles per hour
on this bicycle, through how many revolutions per minute
are the wheels turning?
ω = θ/t
v = s/t
v = rω
The Attempt at a Solution
I know the answer is 452.5 rpm, I looked in the back of the book. I just want to know the method for solving this kind of problem. I have looked at examples in the book, but they didn't have a problem like this solved, so I have no clue how to obtain the correct answer.
Attempts: I used equation v = rω (above), and tired to convert 35 miles to inches (2,217,600 in.), and divide by the radius (13 in), and got:
1. 2,217,600 = 13ω
2. ω = 2,217,600/13 ≈ 170,584
Which is no where near the correct answer. That's is just one of the many methods I tried to use, and at this point I am desperate and frustrated, and I come to you all for help.
Could you describe the steps to solve this problem?