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Velocity of a Rotating Rod

  1. Mar 3, 2008 #1
    Hi guys, I'm new here so thanks for any guidance...
    Using vector notation, I need to find the velocity of an infinte rod, rotating with frequency, ω, centred on the z axis. (rotating about z-axis in the anti-clockwise direction when viewed from above).

    I need to give the velocity in terms of a charge the point r = (x, y, z) which is inside the rod
    (eg r┴ = (√x²+y²) < radius of the rod, a )
    The charge itself is not important, I simply need to find the velocity V of it.

    I have a vague idea as to how to do this:
    I know that the velocity is perpendicular to both r and the z-axis, so it probably involves some sort of cross product?
    Using the unit vector k multiplied by r/|r| ?

    I am pretty clueless with this one guys, despite it only being simple vector manipulation... Any help would be greatly appreciated!
    Thanks in advance
     
  2. jcsd
  3. Mar 4, 2008 #2
    You've got it right, its cross product manipulation. Do you know of any relation between angular velocity and translational velocity?
     
  4. Mar 4, 2008 #3

    tiny-tim

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    Draw a diagram!

    Hi TheFlatlander! Welcome to PF! :smile:

    It often helps to draw a diagram (a rough one).

    Draw a diagram with the x and y axes, and a typical point r.

    Now draw in where r goes during the rotation (I don't mean instantaneously, I mean for the next hour or so).

    You know the frequency (w). Does that tell you how far it goes in any particular time? :smile:

    If so, you have the speed (not the velocity, of course). So what is the velocity? Draw it on the diagram, then write it as a vector.
     
  5. Mar 4, 2008 #4
    Thanks for the tips guys. I got there in the end. :approve:
     
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