A rod of length L0 moves with a speed upsilon along the horizontal direction. Th

Question

A rod of length L0 moves with a speed upsilon along the horizontal direction. The rod makes an angle of theta with respect to the x'-axis. (a) Show that the length of the rod as measured by a stationary observer is given by L = L0[1 - (upsilon2/c2)cos2 theta0]1/2. (b) Show that the angle that the rod makes with the x-axis is given by the expression tan theta = gamma tan theta0. These results show that the rod is both contracted and rotated. (Take the lower end of the rod to be at the origin of the primed coordinate system.)

Explanation / Answer

a) in the horizontal direction, length changes from L0cos0 to Lx = L0cos0(1 - v2/c2)

in the vertical direction, length L0sin0 = Ly has no change.

so the length L = (Lx2 + Ly2) = L0 [cos20 (1 - v2/c2) + sin20] = L0 (1 - cos20*v2/c2)

b) tan = Ly/Lx = sin0/[cos0(1 - v2/c2)] = tan0/(1 - v2/c2) = tan0

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.