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Motion of a lamina

  1. Mar 27, 2006 #1

    I'm not sure if this mechanics question should be in the Maths forum or the physics forum :confused: Nevertheless, I apologise first if I have posted in the wrong area :frown:

    I was wondering if anyone could help me with the following question.

    A lamina moves in its own O(x,y) plane. At a certain instant the displacement from one of its points P to another point Q is (-5i+10j). If the velocity of P is (7i-2j) and the velocity of Q has 5 as its x component:

    1) What is the angular velocity of the lamina?
    2) What is the velocity of Q?

    In my notes I have been given the following equation:

    [tex]v_Q[/tex] = [tex]v_P[/tex] + [tex]\\omega\\[/tex] + [tex]\\vec{PQ} [/tex]

    I've got the information for velocity of P and the displacement but I'm not sure how to express the velocity of Q in vector format? And how to I find the angular velocity? Is it just rearranging the equation for omega? :confused:

    Please help, thanks!
    Last edited: Mar 27, 2006
  2. jcsd
  3. Mar 27, 2006 #2


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    the givens are [tex]v_P=7i-2j,\vec{PQ}=-5i+10j[/tex] and of [tex]V_Q[/tex], we know only the x-component, which is 5, so [tex]V_Q=5i+yj[/tex] where y is unknown. I think you mean to put your equation as

    [tex]v_Q=v_P+\omega +\vec{PQ}[/tex]

    so we have [tex](5i+yj)=(7i-2j)+\omega+(-5i+10j)[/tex]

    EDIT: The angular velocity [tex]\omega[/tex] a vector: for it must be.

    Are, in fact, [tex]v_Q,v_P[/tex] the velocities of Q and P?
    Last edited: Mar 27, 2006
  4. Mar 27, 2006 #3
    Oh yeah, sorry I'm terrible at using Latex :redface: Yep thats the equation I meant.

    Erm in my notes it says that the vector [tex]\omega[/tex] is = theta (with a dot on the top) k i.e its a vector

    Yer [tex]v_Q,v_P[/tex] are the velocities of Q and P.
    Last edited: Mar 27, 2006
  5. Mar 27, 2006 #4


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    I didn't get the 3-D part until just... well then:

    So we should have

    [tex](5i+yj+zk)=(7i-2j)+\vec{\omega} +(-5i+10j)[/tex]

    where y and z are unknown. Still not enough. You need more equations. Dig.
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