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Seemingly simple kinematics exercise

  1. May 18, 2013 #1
    1. The problem statement, all variables and given/known data
    Rigid body
    The plane rigid body ABCD shown in the figure has rectangular shape and
    slides along the orthogonal runners X, Y. The points A and B are always in
    contact with the ranners.
    Data: ω=3 rad/s (angular velocity counterclockwise); [itex]\Theta[/itex]=30°; AB=CD=1m;
    AD=CB=0.5m.
    Determine:
    The A and C velocities;
    The position of instantaneous rotation center;
    The value of [itex]\Theta[/itex] for which the horizontal velocity component of D is null.

    30vke4h.jpg

    2. Relevant equations

    Fundamental geometric identities


    3. The attempt at a solution

    Without knowing the center of rotation or the relevant velocities a priori I don't know how one can be solved for the other. So really, I can't make it past the first step.

    The instructor gave us this solution which to me makes no sense.

    2n86kox.jpg

    He claims that Va = Va/b + Vb

    and that Va/b = ω*AB

    But this makes no sense since it assumes the center of rotation is at point B, or else Va/b wouldn't be given as the product of ω times the length of segment AB.

    Am I missing something or did the instructor forget to inform us that ω refers to point B?
     
    Last edited: May 18, 2013
  2. jcsd
  3. May 18, 2013 #2

    CWatters

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    Homework Helper

    I may not get chance to come back to this for a few days and I'm not even 100% sure but...

    Lets call the instantaneous center of rotation point O. I believe the walls must be tangential/right angles to OB and OA.
     
  4. May 18, 2013 #3
    Here's the (sloppy) solution as given to us. Does this make any sense?
     

    Attached Files:

  5. May 18, 2013 #4
    Hrm, I was completely overlooking the fact that in rigid bodies and angular velocity and angular acceleration are independent of the reference point of the body.

    It makes sense now.
     
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