1. The problem statement, all variables and given/known data A rigid rod has rest length L0 and moves relative to a system S' for which it's coordinates is x'=0, y' = b-ut', z' = 0. In this reference frame the rod is at all times parallel with the x'-axis. a) A point (A) on the rod is measured to be a distance= a, away from x' = 0 in S'. What are the time dependent coordinates of this point in the same reference frame? b) The inertial frame S moves with velocity v along the x axis of another inertial frame S. (The axes of the two frames are parallel.) Find the time dependent coordinates (x, y, z) of the point A in this reference frame. c) What is the orientation of the rod relative to the coordinate axes of S, and what is the length of the rod measured in this frame? 2. Relevant equations Lortenz transformations 3. The attempt at a solution a) In the S' frame the coordinates of this point should obviously be x'= a, y' = b-ut', z'=0. b) Since the x-axis of S' moves with velocity v along the x-axis of S the x coordinate is given by the lorentz transformation as x = G(a + vt'), where G = G(v) is the lortenz factor. I am not completely sure about the other coordinates, but I think that since there are no relative motion between the two frames in the y-directions y = y' = b- ut', but the time coordinates still disagree by t' = G(t -(v/c)a), and z = z' = 0. c) Intuitively it would make sense that the rod has the same orientation in both of the frames. Since the y coordinates of both the point (A) and the middle of the rod should agree this means that the rod is also parallel in the frame S. However the rod is length contracted in the x-direction as measured in S, by L0/G. - Are these arguments correct? What I worry about is the additional motion of the rod along the y-axis. I first thought about introducing a third system moving along with the rod in that direction, but that would introduce an additional time coordinate. So is the argument that since there is no relative motion between S and S' in the y-direction their respective y-coordinates will agree?