1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Collisions in the centre of mass frame

  1. Jan 9, 2012 #1
    I've just found out that in the centre of mass frame, the angle of deflection in a collision is different from in the lab frame.

    I vaguely understand why: if the frame you viewed the particles in was also moving but only horizontally it would make their horizontal movement appear to decrease while their vertical movement would stay constant, which would seem to decrease the angle.

    I have no idea how you would go about finding angles of deflection in the centre of mass frame. Could someone help me derive/ tell me a formula for doing so?
  2. jcsd
  3. Jan 9, 2012 #2


    User Avatar
    Science Advisor

    The angle is a free parameter. The issue is transforming between the frames.
  4. Jan 9, 2012 #3
    How would I go about transforming between frames?

    Thanks for helping! :-)
  5. Jan 9, 2012 #4

    Philip Wood

    User Avatar
    Gold Member

    Call one set of axes S. Let another set of axes, S', be co-incident with S. Let S' now move steadily in the +x direction, relative to S. Now suppose there's a particle moving with velocity components ux, uy, uz as described on the S axes. On the S' axes the components will be (ux-v), uy, uz. This is a galilean (non-relativistic) transform.

    From the components you can find the direction cosines of the velocity vectors in the two frames. If the particle is moving in, say, just the x and y directions then it's even easier: in S, tanθ = uy/ux, whereas in S', tanθ' = uy/(ux-v)
  6. Jan 10, 2012 #5
    Ah, I think I get it now- thanks.
  7. Jan 10, 2012 #6

    Philip Wood

    User Avatar
    Gold Member

    Good! Despite my forgetting to say that v was the velocity of the S' frame relative to the S!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook