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Relative Motion using Rotatin Axis

  1. Apr 29, 2009 #1
    1. The problem statement, all variables and given/known data
    While the bridge is closing with a constant rotation of .5 rad/s, a man runs along the roadway such that when d=10ft, he is running outward from the center at 5 ft/s with an acceleration of 2 ft/s^2, both measured relative to the roadway. Determine his velocity and acceleration at this instant.


    2. Relevant equations

    V(a) = V(o) + Omega X r(a/o) + v(a/o)
    A(a) = A(o) + Omega' X r(a/o) + Omega X (Omega X r(a/o)) + 2Omega X V(a/o) + A(a/o)


    3. The attempt at a solution

    V(o) = 0, Omega = .5k, Omega' = 0, r(a/o) = 10j, V(a/o) = -5j, A(a/o) = -2j

    Lets do velocity first

    Omega X r(a/o) = -5i

    V(a) = 0 + -5i + -5j = -5i - 5j ft/s


    Now Acceleration

    Omega' X r(a/o) = 0
    Omega X (Omega X r(a/o)) = 2.5j
    2Omega X v(a/o) = 5j

    A(a) = 0 + 0 + 2.5j + 5j + -2j = 5.5j ft/s^2


    Shouldn't the velocity and acceleration be in the same direction.
     

    Attached Files:

  2. jcsd
  3. Apr 29, 2009 #2

    Chi Meson

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    No, they rarely are in the same direction. Think about circular motion: what's the direction of the tangential velocity, and what is the direction of centripetal acceleration? (the names give away the answer)
     
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