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Centripetal acceleration and circular motion

  1. Feb 9, 2014 #1
    My question is about the centripetal acceleration formula |a| = ω^2*r. If we keep the angular speed constant then why does increasing the radius increase the centripetal acceleration? I don't find this intuitive because the velocity vector is being turned by the same amount each second, if ω is constant.

    Also is there an intuitive way to think about how the units (m/s^2) relate to circular motion?
  2. jcsd
  3. Feb 9, 2014 #2


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    The linear velocity = ω * r. If r increases, then so does the linear velocity. Using the other form for centripetal acceleration:

    |a| = ω^2 * r = v^2 / r

    If r increases by a factor "c" and ω remains constant, then:

    |a| = ω^2 * c * r = (c * v)^2 / (c * r) = c * v^2 / r
  4. Feb 9, 2014 #3


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    If ω is constant, the particle has to get from one side of the circle to the other in the same amount of time, ∏ω seconds.

    The distance traveled "across the circle" is proportional to r, so it makes sense that the acceleration has to be bigger when r is bigger.
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