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I Need Help With This Problem

  1. Mar 15, 2012 #1
    1. The problem statement, all variables and given/known data

    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?


    2. Relevant equations


    • ω = θ/t

    • v = s/t

    • v = rω

    3. 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.
     
    Last edited: Mar 15, 2012
  2. jcsd
  3. Mar 15, 2012 #2

    jedishrfu

    Staff: Mentor

    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
     
  4. Mar 15, 2012 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    "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?

     
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