Posted by **Jennifer** on Sunday, March 13, 2011 at 6:42pm.

A rod of length 1m lies in the lab frame making angle θ=30 with the

x-axis. Find the length and the angle it makes with the x’-axis as seen by

an observer moving at u=0.8c along the y-direction.

- Physics -
**drwls**, Sunday, March 13, 2011 at 6:53pm
The projection along the x axis, L*cos30, will not change due to relative motion, but the projection along the y axis will be shortened to

L*sin30*sqrt(1-(0.8)^2) = (L/2)*0.6 = 0.3 L

The new length is

L' = sqrt[(Lcos30)^2+(0.3L)^2]

= L*sqrt[.75 + .09] = 0.917 L

The new angle with the x axis is

arctan (0.3/0.866) = 19.1 degrees

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