I'm stuck on this problem in the "Relativistic Particle Mechanics" section, number 26. I had no trouble with the first part... but the second part I'm stuck.(adsbygoogle = window.adsbygoogle || []).push({});

"Two identical particles move with velocities +-u along the parallel lines z=0, y=+-a in a frame S, passing x=0 simultaneously. Prove that all centroids determined by observers moving collinearly with these particles lie on the open line-segment x=z=0, |y|<ua/c"...

I had no trouble here. But now:

"Also prove that, keeping the same total (relativistic) mass and angular momentum, two such particles cannot move along lines closer than 2ua/c without breaking the relativistic speed limit."

My basic idea was to use the equation for conservation of relativistic mass leading to:

[tex] \gamma (v_1) + \gamma (v_2) = 2*\gamma (u)[/tex]

And conservation of 3-angular momentum which leads to:

[tex] \gamma (v_1)*v_1*r_1 + \gamma (v_2)*v_2*r_2 = 2*\gamma (u) * u * a[/tex]

to try and show the required inequality, but haven't been successful. I'd appreciate any help. Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question from Rindler's Introduction to Special Relativity

**Physics Forums | Science Articles, Homework Help, Discussion**