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I Deriving maximum velocity in a rotated frame

  1. Jun 21, 2016 #1
    rotate%20frame_zps6lbjzvxf.jpg
    I have a particle that travels in the cartesian plane with the maximum velocity of A units along the x-axis and B units along the y-axis per unit of time.

    How do I go about deriving the maximum velocity of my particle in the rotated uv plane? (the maximum distance the particle can along the u and the v axes in one unit of time)

    Any tips greatly appreciated.
     
  2. jcsd
  3. Jun 21, 2016 #2
    Hi jumbo:

    I suggest it might help if you add an arrow in the diagram to represent the vector M from the origin to point (x=A,y=B). Then draw perpendiculars from (A,B) to the axes u and v. If you know the angle between x axis and u axis, you can calculate the length of the perpendiculars to the u axis and v axis which represent the M coordinates with respect to the v axis and u axis respectively.

    Hope this helps.

    Regards,
    Buzz
     
  4. Jun 22, 2016 #3
    Thanks Buzz Bloom.

    Is this what you mean?

    vel_max_zpsuvcup2vg.jpg

    Where the length of A' is the maximum distance my particle can travel along the u-axis of the rotated frame in one unit of time. Similarly, the length of B'...
     
    Last edited: Jun 22, 2016
  5. Jun 23, 2016 #4
    Hi jumbo:

    I apologize for not expressing my thought more clearly.

    You want to draw a line, call it L, from the origin to the point M. M will be on the vertical green line at the height B. L represents the vector corresponding to the maximum velocity of the particle you are describing.

    Next draw lines from the point M perpendicular to the u and v axes. These lines will show the coordinates of the vector L in the (u,v) coordinate system. The resulting diagram should help you figure out how to calculate the u and v coordinates of the vector L.

    By the way, for the particular example you have drawn, you may want to notice that the v coordinate of L is negative.

    Hope this helps.

    Regards,
    Buzz
     
  6. Jun 24, 2016 #5
    I think I got it. Thanks Buzz

    vel_max_2_zpscfsvfczk.jpg
     
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