Chapter 38, Problem 18P

A rod moving with a speed v along the horizontal direction is observed to have length ℓ and to make an angle θ with respect to the horizontal as shown in Figure P38.17. (a) Show that the length of the rod as measured by an observer at rest with respect to the rod is ℓ_p = ℓ[1−( v²/c²) cos² θ]^1/2_. (b) Show that the angle θ_p that the rod makes with the x axis according to an observer at rest with respect to the rod can be found from tan θ_p = γ tan θ. These results show that the rod is observed to be both contracted and rotated. (Take the lower end of the rod to be at the origin of the coordinate system in which the rod is at rest.)