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!

Parallel axis theorem for area

  1. Nov 5, 2015 #1
    1. The problem statement, all variables and given/known data
    why the y bar is 0 ? according to the diagram , y ' has certain value , it's not 0 ! can someone help to explain ?

    2. Relevant equations


    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Nov 5, 2015 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    [itex]\overline{y}= 0[/itex] because the y' axis, not the y axis, is defined as the vertical line passing through the center of mass.
     
  4. Nov 5, 2015 #3
    it pass thru centroid , why it is 0 ?
     
  5. Nov 5, 2015 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The shape can be thought of as made up of many little areas like A. Each little area has its own (x', y') coordinates relative to the centroid. y-bar is here defined as the average value of y' across all these little areas. By definition of centroid, that average is zero.
     
  6. Nov 5, 2015 #5
    why only the second integral = 0 , why not the first integral equal to 0 also ?
     
  7. Nov 5, 2015 #6

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Because in the first integral, y' is squared.

    When y' is by itself, you are adding products of y' dA on either side of the centroidal axis, so some products are negative and some are positive. When you calculate y'2 dA, all of the products are positive, so their sum adds up to a positive, non-zero result.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Parallel axis theorem for area
  1. Parallel axis theorem (Replies: 6)

Loading...