1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted