Finding bicycle wheel RPM from speed and diameter

[Soda]

Homework Statement

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?

Homework Equations

• 
  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?

Thanks.

 

[jedishrfu]

why not go back to first principles?

in one hour you traveled 35 mi.

bicycle tire is 26 inch diameter ==> using pi*Diameter = tire circumference

convert (dist traveled) to inches for a common measurement

(dist traveled) / (tire circumference) = revolutions in one hour

(revolution in one hour) / 60 mins = # rpms

 

[HallsofIvy]

Homework Statement

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?

Homework Equations

• 
  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

"v" is the velocity of a point on the circumference of the wheel, not a distance so it makes no sense to replace v with 35 "miles", even converted to inches. If the cycle is going at "35 miles per hour", how far will it go in one minute? The wheel has diameter 26 in so what is its circumrference? What part of that circumference is the distance the cycle goes in one minute?

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?

Thanks.