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I'm solving this problem in which the rod with length $L_0$ is moving at speed v along the horizontal direction; this rod makes an angle $\theta_0$ with the x-axis and I am supposed to determine the length of the rod as measured by the stationary reference frame.
I started with breaking the Length of the rod into horizontal and vertical components; the horizontal component will get contracted for sure, but I am not sure if the vertical component also will contract or not? Is length-contraction multi-dimensional?

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The component that is seen contracted by a moving frame, is along the direction of the velocity of the frame. In your case since the rod is seen to be moving in the horizontal direction, therefore only the horizontal component contracts and not the vertical one.

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  • $\begingroup$ Thank you for your answer! Does that mean that if the rod is observed to be moving along that theta direction it will contract both horizontally and vertically? $\endgroup$ Apr 11, 2022 at 14:06
  • $\begingroup$ Yes, precisely. Also, if you change your axes (by simple rotation), you can have the rod contracting purely along one of the axis directions. This tells us that the physical picture doesn't change based on what you call as horizontal and vertical. $\endgroup$ Apr 11, 2022 at 14:13
  • $\begingroup$ However, in the case of an object with extent in all 3 dimensions (e.g. automobile), there is a parallelogram-like distortion in addition to length contraction. $\endgroup$ Apr 11, 2022 at 14:32

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