1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Finding the Centroid of the surface of a hemisphere

  1. Nov 20, 2011 #1
    Hi gang, I was given this question, but I can't quite seem to get it all the way...
    1.Determine the coordinates of the centroid of the surface of a
    hemisphere, the radius of which is r, with respect to its base.

    2. Relevant equations
    A=2[itex]\pi r^{2}[/itex]
    A: Surface Area of the Hemisphere.

    Coordinates of the centroid: ([itex]\overline{X}, \overline{Y}, \overline{Z}[/itex])

    [itex]\overline{Y}A = \int ydA[/itex]

    I set up the coordinate system so [itex]\overline{X}[/itex] = 0 and [itex]\overline{Z}[/itex] = 0

    3. The attempt at a solution
    I tried finding the circular elements of the hemisphere

    r[itex]_{el}[/itex]: Radius of the element


    Then I used [itex]\overline{Y}( 2\pi r^2) = \int^{r}_{0} y 2 \pi \sqrt{r^2-y^2} dy[/itex]
    but I'm pretty sure this is wrong, any ideas or pointers? Thanks in advance.
  2. jcsd
  3. Nov 20, 2011 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    There's a sneaky, roundabout way to this:

    1. Compute the work needed to assemble the hemisphere from elements of mass dm. The hemisphere when finished sits on its flat base. An element of mass dm is attracted to the earth center by a force g*dm, and work to put it in place = gy*dm where y is height above ground for the element dm.

    2. Then the centroid must be at height h such that Mgh = total work needed to assemble the hemisphere, where M = mass of entire hemisphere.

    Even if you don't want to submit the answer this way, you can double-check your result by this relatively easy integration.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Finding Centroid surface Date
Find the current using Nodal Analysis Yesterday at 6:49 AM
Finding the magnitude of the voltage gain in dB Wednesday at 11:27 AM
Find the Thevenin Equivalent circuit Wednesday at 3:12 AM
What does it mean to find the centroid of a shape? Feb 6, 2016
Composite Bodies: Finding the Centroid Oct 5, 2012