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Angular Distance

  1. Nov 13, 2013 #1
    1. The problem statement, all variables and given/known data
    When driving Bob turns the steering wheel so the distance his hand moves on the steering wheel's circumference is equal to twice the radius of the steering wheel. In both radians and degrees, what angular distance (Δθ) did the wheel turn?


    2. Relevant equations
    S=r*Δθ
    C=2∏r
    1 rev=2∏ rad=360°


    3. The attempt at a solution
    I know the ratio of the circumference to the radius is 2∏. My first attempt I tried to equate the S and C equations. 2∏r=r*Δθ which got rid of r and I did (1/2)(2∏) which just gave me pi and was wrong. I'm not sure how to solve this but I feel like I'm just missing something small.

    I tried making up numbers to help me see it. I pretended r was 5. What I want is 2r, which would be 10. So C=2∏r=31.416. If I divide that by 2∏ I get just r. If I divide it by ∏, I get 2r. So it's still wrong and I'm not sure where to go from here. Any help is really appreciated, it bothers me that I'm missing something.
     
  2. jcsd
  3. Nov 13, 2013 #2

    Mentz114

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    Gold Member

    If the drivers hand moves exactly r in distance, then the angle would be 1 radian, from the definition of the radian. So twice that distance gives 2 radians.
     
  4. Nov 15, 2013 #3
    So it has nothing to do with pi. Well I feel silly ha.
    Thank you for your help.
     
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