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!

Spherical, Cyndrical or Polar Coordinates

  1. Dec 17, 2012 #1
    Spherical, Cylindrical or Polar Coordinates

    1. The problem statement, all variables and given/known data
    I have attached an image of the problem.

    I know that the solution is number 1 but I'm having some difficulty understanding why. In solution one is it using cylindrical coordinates> My first response to this question had been to use spherical coordinates. Would it have been correct to use spherical coordinates if the [itex]\sqrt{}2-x^2-y^2[/itex] had instead been [itex]\sqrt{}1-x^2-y^2[/itex]

    Any input would be greatly appreciated.

    2. Relevant equations



    3. The attempt at a solution

    I know that the solution is number 1 but I'm having some difficulty understanding why. In solution one is it using cylindrical coordinates? Because my first response to this question had been to use spherical coordinates. Would it have been correct to use spherical coordinates if the [itex]\sqrt{}2-x^2-y^2[/itex] had instead been [itex]\sqrt{}1-x^2-y^2[/itex]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

    Last edited: Dec 18, 2012
  2. jcsd
  3. Dec 18, 2012 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Two forms are offered using spherical coordinates, two using cylindrical. In principle, any or none of them could have been correct reformulations of the original integral, but they have been constructed so that only one is correct. You just have to play around converting the original various ways until you can decide which one.
    The nature of the z bound in the original integral does suggest spherical as the most natural, but that's not what the question is about.
     
  4. Dec 18, 2012 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Spherical, Cylindrical or Polar Coordinates

    It should be easy to see that [itex]z= \sqrt{1- x^2+ y^2}[/itex] is the upper half of a sphere with center at (0, 0, 0) and radius 1 while [itex]z= \sqrt{2- x^2+ y^2}[/itex] is the upper half of a sphere with center at (0, 0, 0) and radius [itex]\sqrt{2}[/itex].

    Because they are both parts of spheres, yes, spherical coordinates would be appropriate.

     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Spherical, Cyndrical or Polar Coordinates
Loading...