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Tangential and radial components of acceleration - answer seems odd

  1. Oct 27, 2008 #1
    1. The problem statement, all variables and given/known data
    A 60 cm diameter wheel accelerates uniformly about its center from 120 rpm to 300 rpm in 5s.
    1) Determine its angular acceleration.
    2) Determine the radial component of the linear acceleration of a point on the edge of the wheel 2s after it has started accelerating.
    3)Determine the tangential component of the linear acceleration of a point on the edge of the wheel 2s after it has started accelerating.


    2. Relevant equations
    1) alpha=w2-w1/delta(t)
    2 and 3) w'=w+alpha t'
    v=Rw'
    radial component=v^2/r
    tangential component =alpha r
    BUT alpha=radial+tangential


    3. The attempt at a solution
    1) I determined that alpha = 3.77rad/s^2
    2)w'=120*2pi/60 + 3.77*2s
    w'=20
    v=.6/2*20 = 6
    radial = 6^2/.3 = 120 m/s^2
    this seems very high!! shouldn't it be less than 3.77?

    3) tangential = 3.77*.3 = 1.131 m/s^2
     
  2. jcsd
  3. Oct 27, 2008 #2

    Redbelly98

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    Your numbers look right to me. There's no reason or sense in comparing a_radial to alpha when they don't even have the same units. I.e., 120 m/s^2 is neither less than, equal to, or greater than 3.77 rad/s^2.

    EDIT:
    Looks like you wrote w' when you probably meant w (or ω), the rotation rate in rad/s.
     
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