A rod moving with a speed v along the horizontal direction

Chapter 39, Problem 30

(choose chapter or problem)

A rod moving with a speed v along the horizontal direction is observed to have length , and to make an angle u with respect to the direction of motion as shown in Figure P39.29. (a) Show that the length of the rod as measured by an observer at rest with respect to the rod is ,p 5 ,[1 2 (v 2 /c 2) cos2 u]1/2. (b) Show that the angle up that the rod makes with the x axis according to an observer at rest with respect to the rod can be found from tan up 5 g tan u. 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.)