I'm trying an exercise from D'Inverno book "Introducing Einstein's Relativity" that says

S and S' are in standard configuration with $v = \alpha c$ $(0 < \alpha < 1)$. If a rod at rest in S' makes an angle of 45º with Ox in S and 30º with O'x in S', then find $\alpha$.

Well, I tried to do this thinking that there is an angle between the axis of the frames, i.e., 45º - 30º = 15º. But as they are in 'standard configuration', it means that the axis are parallel (and that the movement of S' is in the direction of positive x axis). So I don't see how the movement of S' with respect to S influences on the orientation of the rod from one frame to another. Any help in understanding this will be appreciated.

Note: The answer is $\alpha = (2/3)^{\frac{1}{2}}$

  • $\begingroup$ Think about length contraction along the direction of relative motion. $\endgroup$ – G. Smith Jun 16 at 20:58
  • $\begingroup$ Yes, I got it! Thank you! $\endgroup$ – Elismar Lösch Jun 16 at 21:27

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