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Motion about a moving axis

  1. May 15, 2007 #1
    In a motion about a fixed axis, where the position is r(t) and the angular velocity is w(t), we know that dr/dr = w(t)xr(t).
    My question, does this equation remains true if the axis vector is changing by the time t? Why so?
    Thank you.
     
  2. jcsd
  3. May 15, 2007 #2

    Mentz114

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    Gold Member

    Do you mean dr/dt ? I'm not clear about the description.
     
  4. May 15, 2007 #3
    Yes, dr/dt.
    r(t) = r0*R+h0*D
    Where r0 is a constant distance scalar, and h0 is the distance from the plane that D is normal to.
    D is a unit vector, the axis of rotation, so the particle rotates around the axis D. And R is a unit vector, which is the radial vector. R is the opposite direction of the centerpital accelaration.
    R is dependant of t, the time.
    On a motion around a fixed axis, D is a constant vector, and in this case:
    dr/dt = r0*dR/dt = wxr
    My question is, what happens when D is not a constant, but instead D(t) is a vector dependant of the time t?
    Is it still true that dr/dt = wxr?
    Where w is the angular velocity.
     
  5. May 15, 2007 #4

    Mentz114

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    Yetar, I'm sorry I can't answer your question. Maybe someone else can help.
     
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