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Tangential acceleration of a bicycle pedal

  1. Jan 12, 2013 #1
    I'm attempting to solve a mastering physics problem, but I've seem to run into a dead-end on this problem. I've worked out my solution and I'm certain I've rounded my sig figs correctly, but mp doesn't accept the answer.

    1. The problem statement, all variables and given/known data
    An 17-cm long bicycle crank arm, with a pedal at one end, is attached to a 24-cm diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling rate from 64rpm to 95rpm in 12 seconds.


    2. Relevant equations
    α tangential = αt = α * radius
    α = dω/dt


    3. The attempt at a solution
    a. put terms in rpm into rad/sec
    ωi = 64 rpm
    ωf = 95 rpm
    ωi = 64 (1 rotation / 1 minute) * (2∏ rad / 1 rotation) * (1 minute / 60 sec) ≈ 6.702 rad/sec
    ωf = 95 (1 rotation / 1 minute) * (2∏ rad / 1 rotation) * (1 minute / 60 sec) ≈ 9.948 rad/sec

    b. calculate rotational acceleration
    α = (ωf - ωi) / time difference
    α = (ωf - ωi) / 12 sec
    α ≈ 0.271 rad/sec2

    c. calculate tangential acceleration of the pedal
    αt = α * radius
    αt ≈ 0.271 rad/sec2 * 17 cm
    αt ≈ 0.271 rad/sec2 * 0.17 m
    αt ≈ 0.046 m/sec2

    Does anybody know what I'm doing wrong in my reasoning? Or am I not understanding the mechanics of a bicycle correctly?

    Thanks in advance
     
    Last edited: Jan 12, 2013
  2. jcsd
  3. Jan 12, 2013 #2

    haruspex

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    Your working all looks correct. You didn't state the actual question, e.g. what units the answer is to be in.
    If it asks for three sig figs I would answer 0.0460.
     
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