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

Is this force a central field ?

  1. Sep 26, 2004 #1


    User Avatar

    Is this force a "central field" ?

    A partical moves in a spiral orbit given by:


    if [tex]\theta[/tex] increases linearly with time, is the force a central field? If not, how would [tex]\theta[/tex] have to vary with time for a central force?

    I believe that a central force is a function only of the scalar distance, r, to the force center, and its direction is along the radius vector.

    I also believe that the angular momentum of a particle is constant when it is moving under the action of a central force.

    Even though I seem to remember the above, I'm at a loss see whether or not the above is a central force -- nor how to modify it to make it one??
  2. jcsd
  3. Sep 26, 2004 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What is the angular momentum, in terms of r and \theta ?
  4. Sep 26, 2004 #3


    User Avatar

    [tex]L = r \times mv = mr^2\dot{\theta}[/tex]

    I think ...

    So, this means

    [tex]L = r \times mv = mr^2\dot{\theta} = ma^2\theta^2\dot{\theta}[/tex]

    [tex]\dot{\theta}[/tex] is constant (since it varies linearly with t), but [tex]\theta^2[/tex] is not constant.

    So -- this does not correspond to a central field? Or am I still missing something?
  5. Sep 26, 2004 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    From the trajectory, you can calculate the velocity vector and the acceleration vector. [Using Newton's Law, you can find the force vector.] You can express this as a vector field. Check if its curl is zero... (I believe this is necessary but not sufficient for a central force).

    Of course, you can probably just check if the acceleration vector is radial.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Is this force a central field ?
  1. Central force (Replies: 1)