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: Density and circumference relationship? From Example in book

  1. Dec 19, 2016 #1
    1. The problem statement, all variables and given/known data
    Example 5.3 from The Marion Thornton book (fifth edition) of Classical Dynamics states the following problem:

    Consider a thin uniform circular ring of radius a and mass M. A mass m is placed in the plane of the ring. Find a position of equilibrium and determine whether it is stable.

    I'm following the example in the book, and there's two things I don't understand. First is why /rho = \frac{M}{2*/pi * a}. I always thought that the density was the mass over the volume, so I don't see why this is mass over circumference.

    Second, in the next piece, it says that d\Phi = -G \frac{dM}{b} = \frac{-Ga\rho}{b}d\phi

    I'm failing to see two things. 1) why the dM element ends up with a small phi, and 2) why rho is as it is. From here, I believe I can find the rest of the example, but why are these two things true?
  2. jcsd
  3. Dec 20, 2016 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    The textbook is apparently using the symbol ##\rho ## to denote the linear mass density.

    An infinitesimal arc length can be written in terms of ##d \phi##.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted