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: Center of mass of a lamina

  1. May 5, 2013 #1
    1. The problem statement, all variables and given/known data
    The boundary of a lamina consists of the semicircles [itex]y=\sqrt{1-x^{2}}[/itex] and [itex]y=\sqrt{4-x^{2}}[/itex] together with the portions of the x-axis that join them. Find the centre of mass of the lamina if the density at any point is proportion to its distance from the origin.

    2. Relevant equations

    3. The attempt at a solution
    My issue here is only in turning the statement "the density at any point is proportion to its distance from the origin" into a function.

    The solution is [itex]f(x,y)=k\sqrt{x^{2}+y^{2}}[/itex] but why are they ignoring Z here? Since the lamina is in 3D right?

    If I try turn this statement into a function I get [itex] f(x,y) = k\sqrt{f(x,y)^{2} + x^{2} + y^{2}}[/itex] which doesn't work. Where have I gone wrong in my thinking?
  2. jcsd
  3. May 5, 2013 #2


    User Avatar
    2017 Award

    Staff: Mentor

    The shape is given as a 2D-object. How did you get the second equation, and what does it represent?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted