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Rotate about an axis

  1. Jun 12, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex]A = (1,1,-2)[/tex]
    [tex]C = (0,1,-5)[/tex]
    (in cartesian coordinates)
    Let A and C be drawn from a common origin and let C rotate about A with an angular velocity of 2 rad/s. Find the velocity of the head of C.

    2. Relevant equations

    [tex]v = w x r[/tex]

    3. The attempt at a solution
    w = 2 rad/s
    I know I have to take the cross product of w and C (w x C = v) but I am having problems making w as a vector. Initially I thought I would use cylindrical coords and say that it's moving in the phi direction, unfortunately I don't know if that assumption is correct.
    Can anyone give me a pointer on how I should begin to write w as a vector?
  2. jcsd
  3. Jun 12, 2008 #2
    If by w you mean [itex]\omega[/itex], the angular velocity, then the direction of omega is always perpendicular on the plane of the speed v. Use the right-hand-rule: If you curl your fingers in the direction of v, then the thumb (stretched out) is the direction of omega.

    For example, the direction of omega for the hands of a clock (assuming they move with constant speed instead of in little jumps) would be into the clock.
  4. Jun 12, 2008 #3


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    Omega points along the axis of rotation. It makes sense if you think about what the cross product does and the relation between omega, r and v.
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