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Dynamics: Angular Acceleration of Rods Connected to Disk

  1. Jul 9, 2011 #1
    1. The problem statement, all variables and given/known data
    Bars BC and AB and dish OA are attached by a pin like in the picture. The dish has a constant angular velocity [itex]\omega\_{0}[/itex]. Find the angular acceleration of bars BC and AB.

    2. Relevant equations
    Relative Motion Equations:
    v[itex]_{b}[/itex]=v[itex]_{A}[/itex]+v[itex]_{A/B}[/itex]
    a[itex]_{B}[/itex]=a[itex]_{A}[/itex]+[itex]\alpha_{A}[/itex]Xr[itex]_{B/A}[/itex]-[itex]\omega^{2}[/itex]r[itex]_{B/A}[/itex]

    3. The attempt at a solution
    So far, I have this written down:

    V[itex]_{A}[/itex]=[itex]\omega[/itex]r
    a[itex]_{A}[/itex]=V[itex]_{A}[/itex][itex]^{2}[/itex]/r=[itex]\omega^{2}[/itex]r

    a[itex]_{B}[/itex]=[itex]\alpha_{BC}[/itex]Xr[itex]_{BC}[/itex]-[itex]\omega_{BC}^{2}[/itex]r[itex]_{BC}[/itex]

    Still just fumbling over these equations. Any help is appreciated.
     

    Attached Files:

    Last edited: Jul 9, 2011
  2. jcsd
  3. Jul 10, 2011 #2

    tiny-tim

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    welcome to pf!

    hi vercingortix! welcome to pf! :smile:

    (have a theta: θ and an omega: ω :wink:)

    (centripetal acceleration is irrelevant)

    ω = (vP - vQ)/PQ

    so find vB as a function of θ :wink:
     
  4. Jul 10, 2011 #3
    That equation looks foreign to me. What I'm currently trying to do is solve for angular acceleration of the bar by knowing the omega and accelerations of both A & B. Something like the second equation in my original post. I'm very lost.
     
  5. Jul 11, 2011 #4

    tiny-tim

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    hi vercingortix! :wink:

    ω = |vP - vQ]/PQ

    and

    α = |aP - aQ|/PQ

    are the definitions of angular speed and acceleration

    so find the x,y components of B as a function of θ, and differentiate to get vB and aB :smile:
     
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