Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Conservation of linear momentum at relativistic speeds

  1. Oct 5, 2003 #1
    The question I ask is linear momentum conserved in
    in instance cited below?

    You place a particle at the origin on a x-y axis
    and accelerate it to 61% of c in the y direction.
    Then you accelerate it to 61% of c in the x direction.
    The net velocity of the particle will be
    86% of c at 45 degrees.The key here is that it
    takes approximately 3 times the energy to
    accelerate the particle in the x direction than
    the y direction, due to the fact that the net
    velocity change in the y direction is 0%-61% of c
    and in x direction the net velocity change is
    61%-86% of c.If the rate of acceleration,distance
    of acceleration and time of acceleration are the
    same on the x and y axis, then force of acceleration on
    the x axis has to be greater than
    on the y axis, since the energy of acceleration
    on the x axis is 3 times that of the y axis.
    Therefore the momentum on the x axis is greater
    the y axis.

    If the particle's final velocity is 86% of c at
    45 degrees then the momentum of acceleration
    should be equal on both the x and y axis.
    Is there a discrepancy in momentum here?
  2. jcsd
  3. Oct 7, 2003 #2


    User Avatar
    Science Advisor

    I don't think so. No acceleration above 0.61c is used or provides momentum. The 0.86c is the apparent VECTORED V (in your example). But, I don't think that your example is correct since you seem to be using two-dimensional (graph-paper) trig here, while with excluding time. In V calculations, a Y velocity at 0.61c and an X velocity at 0.61c takes time to reach the "end-point" from where you measure the Hypotenuse. The "actual V" of the vectored triangle cannot exceed the V of the greater of the XV or the YV if time is included. The "apparent" V can though, as is seen in apparent superluminal expansion around some supernova remnants.
    Last edited: Oct 7, 2003
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?