1. Not finding help here? Sign up for a free 30min 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!

Center of mass of a cone

  1. Oct 18, 2005 #1
    I need to find the center of mass of a cone with point facing downwards, of height H and radius R.

    Since the density is constant throughout and because of axial symmetry the center must be somewhere on the z-axis.

    I know from convention that this is H/4 but i need to derive this.

    Rcm = (intregral from 0 to H) of the change in radius

    this is where im stumped
    i did really bad in calculus

    could anyone help me?
  2. jcsd
  3. Oct 18, 2005 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Hint: Consider the cone as a stack of disks.
  4. Oct 18, 2005 #3
    Let Dv Be An Element In The Form Of A Disk That Cuts Through The Cone.

    The Radius Of The Disk Is (r / H) X.

    The Volume Equals The Area Of The Disk Times The Thickness.

    Dv = Pi[(r / H ) X] ^2
    Now Intergate From 0 To H

    X' = Int (x Dv) / Int Dv = 3/4 H
  5. Oct 18, 2005 #4
    okay so the biggest such disk would have volume pi*R^2*h

    what is the volume of the disk under that?
  6. Oct 18, 2005 #5


    User Avatar
    Homework Helper

    the biggest *THIN* disk, at x = H, has radius r = xR/H,
    so its Volume = dV = pi R^2 dx.

    You need to integrate x from 0 to H .
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Center of mass of a cone