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!

I Proof of angular momentum conservation

  1. Aug 6, 2016 #1
    upload.png
    This is from text [Introduction to Lagrangian and Hamiltonian Mechanics] on NTNU opencourse.
    Annnnd... I don't use english as my primary language, so sorry for poor sentences.

    I can't get two things in here.

    First, at (1.12) I can't understand how L dot derivated like that.
    Since I know differentiation of cross product should be done like

    d/dt(AxB)=d/dt(A) x B + A x d/dt(B)

    then, at (1.12), why it doesn't have the terms of d/dt(r) x p ?
    I think it only has the terms of r x d/dt(p)

    Second, I can't get how
    upload2.png
    were derived by using (1.13), How could ri X Fji = 1/2(rij X Fji)
    is possible?

    These might be dumb questions, but please help me.
     
  2. jcsd
  3. Aug 6, 2016 #2
    ##\boldsymbol p_i=m_i\dot{\boldsymbol r}_i,\quad \dot{\boldsymbol r}_i\times\dot{\boldsymbol r}_i=0##
    by the way ##\sum_{ij}{\boldsymbol r}_{i}\times\boldsymbol F_{ji}=0##
     
  4. Aug 6, 2016 #3
    Thank you for clear explanation. Got the first one.

    Yes Σij rij x Fji = 0 so eventually it makes L dot = tau (torque)
    But, what I want know is the mathematical manuever that makes ri X Fji = 1/2(rij X Fji)
     
  5. Aug 6, 2016 #4
    do the calculation for two particles directly and everything will be clear
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Proof of angular momentum conservation
Loading...