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Circular Motion Due to Coriolis Force

  1. Jan 30, 2012 #1
    1. The problem statement, all variables and given/known data

    A particle has velocity v on a smooth horizontal plane. Show that the particle will move in a circle due to the rotation of the earth and find the radius of the circle. (Ignore all fictitious forces except the Coriolis force.)



    2. Relevant equations

    Coriolis force, given by

    FC = -2m(ωxv)


    3. The attempt at a solution

    I started off by writing out the vector ω:

    ωxyz

    But the x component of the earth's angular velocity is zero.

    The velocity of the particle is horizontal, so has no z component.

    So I tried calculating the cross product of ω and v and ended up with:

    FC=-2m[(-ωzvy)i + (ωzvx)j + (-ωyvx)k]

    This is where I got stuck..I'm not sure how I'm supposed to show that this causes circular motion. I'd assume I'm looking for a force perpendicular to v...

    If anyone can give me any advice or let me know what I'm doing wrong I'd appreciate it!
     
    Last edited: Jan 30, 2012
  2. jcsd
  3. Jan 31, 2012 #2
    Find net force on the particle in earths frame. (it may help.i'm not sure.)
     
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