(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A rod of length L_0 moves with a speed v along the horizontal direction. The rod makes an angle of [tex]\vartheta[/tex]_0 with respect to the x'-axis.

(a) Show that the length of the rod as measured by a stationary observer is given by

L = L_0 [1-(v/c)[tex]^{2}[/tex] cos [tex]^{2} ( [/tex] [tex]\vartheta[/tex]_0 ) ] [tex]^{1/2}[/tex]

(b) Show that the angle that the rod makes with the x-axis is given by the expression

tan [tex]\vartheta[/tex] = [tex]\gamma[/tex] tan [tex]\vartheta[/tex]_0.

These results show that the rod is both contracted and rotated. (Take the lower end of the rod to be at the origin of the primed coordinate system.)

2. Relevant equations

[tex]\gamma[/tex] = [1- (v/c)^2]^(-1/2)

(Length contraction formula) L_0 = L / [tex]\gamma[/tex]

3. The attempt at a solution

The horizontal component of the rod in the x'-axis is:

x_0 = L_0 cos ( [tex]\vartheta[/tex]_0 )

Applying the length contraction formula, I was able to show (which differs from what I was supposed to show):

L = L_0 cos [tex]\vartheta[/tex]_0 / [1- (v/c)^2]^(1/2)

I do not understand why this is not the correct answer. I did not attempt the second part of the question.

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# Modern Physics: Length Contraction

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