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Rotating vertical rod

  1. Dec 9, 2016 #1
    1. The problem statement, all variables and given/known data
    A vertical rod is rotating about its longitudinal axis at a constant angular velocity Ω. It is allowed to swing freely from the endpoint A. The angle between the rod and the longitudinal axis of the system is denoted by θ. Point A is located on the highest endpoint of the rod, point B on the lowest.
    On top of the rod there is a disk that is rolling over the rod. The disk cannot fall from the rod or slip at any time. The disk is rotating with an angular velocity of ωrel and velocity vrel.
    The whole system (rod, disk, etc) is moving with a velocity of V.
    I added the problem statement and a figure showing the dynamics and relations relevant for the system.

    2. Relevant equations
    v=Ωxr
    a=Ωx(Ωxr)

    3. The attempt at a solution
    I put a reference frame in the rotating frame with the axis: nhat in the rotating direction, lhat that talways in the direction where the rod is rotating and mhat orthogonal to both nhat and lhat.

    a.)
    Ωrot = Ω nhat
    va = Ωrot x rahat = Ω nhat
    vb = Ωrot x rbhat = -Ω Lcos(θ) lhat
    vab = Ω(1,-Ω Lcos(θ) lhat,0) + vsystem

    b.)
    vc = Ωrot x rchat = -L/2 Ω cos(θ) lhat + vsystem
    ac = Ωrot x(Ωrot x rchat) = -L/2 Ω2 cos(θ) nhat

    Does what I did make any sense or am I completely off?
    Thank you for your time
    IMG-20161209-WA0020.jpg IMG-20161209-WA0022.jpg
     
    Last edited: Dec 9, 2016
  2. jcsd
  3. Dec 9, 2016 #2

    TSny

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    Welcome to PF!
    Did you forget to add these? I don't see them.
     
  4. Dec 9, 2016 #3
    Oh sorry. It didn't upload them. I'll get on the computer and upload them right away. Thanks for noticing
     
  5. Dec 9, 2016 #4

    haruspex

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    Good job you uploaded the original text too. I would never have understood from your rewording that "it" is a different rod.
    Ok so far, but then you lost me. You seem to have started calculating some linear velocities. Part a only wants the angular velocity of rod AB.
    First, define your coordinate frame. I get that ##\hat n## is upwards.
    What other contribution is there to AB's angular velocity?
     
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