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A problem on angles from different inertial frames

  1. Apr 12, 2012 #1
    1. The problem statement, all variables and given/known data

    A rod lies at an angle α with the x'-axis of an inertial frame moving at a speed v along the x-axis(x and x' are parallel) of another inertial frame. The rod makes angle β with the x-axis of this frame. Find the relation between α and β.

    Variables: α,β,v
    and define
    γ=1/√1-(v/c)2;
    x'=projection of rod along x.-axis with respect to first inertial frame;
    z'=projection of rod along z'-axis(perpendicular to x') with respect to first inertial frame;
    x=projection of rod along x-axis with respect to second inertial frame;
    z=projection of rod along z-axis with respect to second inertial frame;


    2. Relevant equations

    Since lengths perpendicular to the relative motion remains unchanged, z'=z;
    According to the second inertial frame, the length of the rod along the direction of motion is contracted by a factor of γ. Thus, x=(1/γ)x'.

    tanα=z'/x' and tanβ=z/x.

    3. The attempt at a solution

    Thus, tanβ=γtanα.

    The problem is, the answer given in the book is, tanα=γtanβ. I am confused, please help.
     
    Last edited: Apr 12, 2012
  2. jcsd
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