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Homework Help: Relative circular motion

  1. Feb 25, 2006 #1
    • Two cyclists( A, B) traveling with the same constant speed, v,
    • in a circular track.
    • They start at the same point on the circle.
    • cyclist B travel through the diameter of the circle, assume the x-axis on a xy
    • Cyclist A travel on the circumference of the circle

    • Find speed of A with respect to B.

    Given: the constant speed, radius, angle between A and the x-axis through the centre, angle between A and B.

    am I suppose to do something with the acceleration (normal/centripedal) and the two angles given.

    thank you
     
  2. jcsd
  3. Feb 26, 2006 #2

    Astronuc

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    It has to do with the velocity of each, and the velocity of A with respect to B is dependent on the angles between the velocity vectors.

    When A and B start, A is moving away from B, and only starts moving toward B after A passes the quarter arc.

    At time t = v/D = v/2R, B moves outside A's circular trajectory.

    [itex]\vec_B[/itex] is always v[itex]\,\hat{x}[/itex], whereas

    [itex]\vec_A[/itex] is always v[tex]\,\hat{\theta}[/tex] where [tex]\hat{\theta}[/tex] is the unit vector in the azimuthal direction (tangent to circumference of circle). As xB gets very large, the angle between A and B gets very small.

    The 'speed' would be the magnitude of the velocity vector given by [itex]\vec_A[/itex] - [itex]\vec_B[/itex]
     
  4. Feb 27, 2006 #3
    Thanks for the reply. It really does look a lot simpler now.

    But when you wrote t= V/D, did you mean t = D/V?
     
  5. Mar 1, 2006 #4

    Astronuc

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    Yes, t = D/V. My mistake.
     
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