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Radial vs Tangential acceleration

  1. Dec 9, 2013 #1
    I ma having a little bit of trouble distinguishing radial and tangential acceleration.

    For example:

    The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:

    A. the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 4
    B. the magnitude of the angular velocity is multiplied by a factor of 4 and the angular accel- eration is not changed
    C. the magnitudes of the angular velocity and the angular acceleration are each multiplied by a factor of 2
    D. the magnitude of the angular velocity is multiplied by a factor of 2 and the angular accel- eration is not changed
    E. the magnitude of the angular velocity is multiplied by a factor of 2 and the magnitude of the angular acceleration is multiplied by a factor of 4
    ans: E

    But if ar = v2/r = ω2r so if angular velocity is multiplied by a factor of 2, this works. But, doesn't αt = ω? So a = α2t2r is also valid, right? Therefore, 2 is also the factor the angular acceleration should be multiplied.

    I realize a = αr, but isn't this tangential acceleration and isn't the question assessing radial acceleration?
    Any help in differentiating the two types of acceleration would great! Thank you :)
     
  2. jcsd
  3. Dec 9, 2013 #2

    TSny

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    Gold Member

    Yes

    The question is asking about the magnitude of the total (or net) acceleration (with contribution from both the centripetal and tangential acceleration).

    [EDIT]
    ω = αt assumes constant angular acceleration. This is not assumed in this problem.
     
  4. Dec 9, 2013 #3
    Oh, thank you! So, then using components, the end result would af/ai = (32/2)1/2 and this gives a factor of 4. Exactly what I was looking for!
     
  5. Dec 9, 2013 #4

    TSny

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    Since I don't know what your reasoning was that led you to af/ai = (32/2)1/2, I can't say if you worked it correctly. But maybe it's fine.
     
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