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: Moment of inertia with varying density

  1. Apr 20, 2007 #1
    I had to find the moment of inertia of a sphere of varying density where the density is some constant times the radius.

    I used the equations from here


    I inserted this d=cr in for the density.

    For the mass I used dm=4(pi)(d)r^2dr, inserted the density, integrated and solved for c.

    After substitution I the answer I got was 2/15mr^2.

    Does this sound right?
  2. jcsd
  3. Apr 21, 2007 #2


    User Avatar
    Gold Member

    The answer should be between the solid sphere value and the thin shell value, so your answer is too small. I did a rough calculation and got 1/2Mr^2.

    Can you show more of your working ?
  4. Apr 21, 2007 #3


    User Avatar
    Homework Helper

    your dm element seems ok if you are taking thin shell as your differential element. I got [tex]\frac{4}{9} MR^2[/tex]. you should check whether you have got constant c correct.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook