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!

Homework Help: Vector calculus question

  1. Oct 17, 2014 #1
    Problem: Consider a system for which Newton's second law is $$ \frac {d \vec v}{dt} = - [ \frac {h(r)h'(r)}{r} + \frac {k}{r^3} ] \vec r- \frac {h'(r)}{r} \vec L $$ where k is a constant, h(r) is some function of r, h'(r) is its derivative and L = r x v is the angular momentum. Show that $$ \frac {d \vec L}{dt} = - \frac {h'(r)}{r} \vec r × \vec L$$ and use this equation to prove that L is not generally conserved, but its magnitude L is conserved.

    Attempt: I've done the first part of the question, but I don't know how I should go about showing that L is not conserved but its magnitude is conserved. Any hints would be appreciated.
     
  2. jcsd
  3. Oct 17, 2014 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The magnitude squared is given by the dot product of L with itself. Can you show the time derivative of that is 0?
     
  4. Oct 17, 2014 #3
    So |L|^2 = (r×v)⋅(r×v) = (rr)(vv) - (vr)(vr) = |r|^2 |v|^2 right? But how would I show the time derivative of this to be 0? [itex] \frac {dL}{dt} = r \frac {dv}{dt} + v \frac {dr}{dt} [/itex], but how do I make this equal 0?
     
  5. Oct 17, 2014 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You want to show the time derivative of ##L \cdot L## is zero. Use the product rule and your given expression for dL/dt. Can you tell me why dL/dt must be perpendicular to L?
     
    Last edited: Oct 17, 2014
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Loading...