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Relativistic Mechanics

Problem 1.342

Find the proper length of a rod if in the laboratory frame of reference its velocity is v=c/2,v=c / 2, the length l=1.00 m,l=1.00 \mathrm{~m}, and the angle between the rod and its direction of motion is θ=45∘\theta=45^{\circ}

Reveal Answer
l0=l(1−β2sin⁡2θ)/(1−β2)=1.08 m, where β=v/cl_{0}=l \sqrt{\left(1-\beta^{2} \sin ^{2} \theta\right) /\left(1-\beta^{2}\right)}=1.08 \mathrm{~m}, \text { where } \beta=v / c
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