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!

Determine if angular momentum is conserved given potential energy funtions?

  1. Jan 27, 2013 #1

    ENT

    User Avatar

    1. The problem statement, all variables and given/known data
    For each of the following potential energy functions in three dimensions, what quantities are conserved (energy, momentum, angular momentum)?


    2. Relevant equations
    U = k/2(x^2 + y^2)

    U = α/r

    U = β(z(hat) dotted with r)^2

    U = α/r + β(z(hat) dotted with r)^2

    Where z(hat) is the unit vector in the z direction.

    3. The attempt at a solution

    So I understand that in order for the angular momentum to be conserved the cross product of r and F, being the force obtained from the negative gradient of U, must be equal to zero. However I am not sure what to use for the position vector r.
     
    Last edited: Jan 27, 2013
  2. jcsd
  3. Jan 27, 2013 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Suppose you measure moment about a point v for a force F acting at r. You know Fxr=0. What will the moment about v be?
     
  4. Jan 27, 2013 #3

    ENT

    User Avatar

    We don't know that F x r = 0. We are trying to determine whether it is or not, and I am not sure what to use for r.
     
  5. Jan 27, 2013 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Yes, sorry, I was thinking specifically of the U = a/r case, but forgot to say so.
    As I read that question, U is specified in relation to a coordinate system where r is the position vector, and the field it defines will be symmetric about the origin. Hence Fxr will be 0.
    For any other reference point v, what is the vector from v to the point r? If the force of the field at r is F(r), what will be its moment about v?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Determine if angular momentum is conserved given potential energy funtions?
Loading...