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Instantaneous Acceleration for Uniform Circular Motion

  1. Mar 19, 2012 #1
    1. The problem statement, all variables and given/known data
    A normally functioning clock has a radius of 30cm. What is the average acceleration in the first 15 seconds if the second hand starts at 12? What is the instantaneous acceleration when the second hand is at 12?


    2. Relevant equations
    v = d/t

    a = Δv / Δt
    limit as Δt approaches 0





    3. The attempt at a solution
    vo = d/t
    vo = (2*r*pi) / t
    vo = (2*30*pi) / 60
    vo = 3.14 cm/s

    v = d/t
    v = (2*r*pi) / t
    v = (2*30*pi) / 60
    v = 3.14 cm/s



    For average velocity between 0 - 15 seconds:

    a = Δv / Δt

    Δv² = v² + (vo
    Δv = 4.44 cm/s [S 45° W]

    a = 4.44 / 15
    a = 0.30 cm/s² [S 45° W]



    I'm not too sure how to find the instantaneous acceleration. I have no idea what a limit is or how to use it.


    a = Δv / Δt
    a = (velocity at 11.999s - velocity at 12.001s) / 12.001 - 11.999


    I'm not sure if this is anything close to being right?
     
  2. jcsd
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