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: Moment of Inertia of Shapes

  1. Apr 16, 2008 #1
    Ok im try to understand how to find the moment of inertia of different shapes by using direct integration. In a lot of the solutions I see they always have this one thing that I dont understand. Example:

    Determine by direct integration the moment of inertia of the shaded area
    with respect to the y axis.

    http://img406.imageshack.us/img406/4816/64329189gz9.jpg [Broken]


    I know the formula is

    Iy = INTEGRALOF(x^2 dA)

    doesnt da = xdy

    so that makes it

    Iy =INTEGRALOF(x^2 * x *dy)
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Apr 16, 2008 #2


    User Avatar
    Homework Helper

    Hi salman213,

    It appears to me that the way they are setting up the integral is by dividing the area into infinitesimal strips of length x and height dy. Each of these strips has the form of a thin rod which is rotating about one end, and that is where the (1/3) comes from. (The moment of inertia of a thin rod rotating about one end is [itex]\frac{1}{3}ML^2[/itex].)

    The integral then sums up the moments of inertia of these strips.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook