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A mechanics problem with moving and fixed coordinate systems

  1. Jan 16, 2014 #1
    1. A point P is described in terms of a fixed coordinate system XYZ with unit vectors I,J,K and a moving coordinate system xyx with unit vectors i,j,k.at a given instant the location of the origin
    of the moving system is 80I-90J.the velocity of P relative to moving system is 50i+45j;the radius of point P is 3i+4j in the moving system, which rotates at angular velocity w=100k. Find the velocity of point P in the fixed system if the x axis is rotated 30 counterclockwise from the X axis.



    2. Relevant equations
    R=R0+r
    R=R0xI+R0yJ+R0zk+rxi+ryj+rzk
    R^=R^0xI+R^0yJ+R^0zK+r^xi+r^yj+r^zk+rxi^+ryj^+rzk^, here ^ represents derivative,i.e it is dot.
    3. The attempt at a solution
    v=wxr , x:cross product symbol v=300j-400i I dont know where I should use this v and its relation with another V which is 50i +45 j as given in the problem.In this problem I dont clearly understand whether w is belongs to radius or moving coordinates.
     
    Last edited: Jan 16, 2014
  2. jcsd
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