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!

Finding the moment(s) of inertia

  1. Mar 27, 2013 #1
    1. The problem statement, all variables and given/known data

    A wedge of a sphere of radius 14 cm (similar to one
    segment of an orange) is oriented so that the axis is aligned
    with the z-axis, one face is in the xz plane, and the other
    is inclined at an angle of α = 29o
    , as shown. The wedge is
    made of metal having a density of 4500 kg/m3
    . In the coordinate system shown, compute a) Ixx, b) Iyy, and c) Izz.

    The picture is attached

    2. Relevant equations

    I know that

    I_xx= ∫(y^2+z^2)ρ dV
    I_yy= ∫(x^2+z^2)ρ dV
    I_zz= ∫(y^2+y^2)ρ dV

    3. The attempt at a solution

    I'm having trouble thinking of how to replace the dV with something in terms of x y and z

    The first thing I did was find the mass, but I'm not sure if it would help at all

    I did V=4/3 π r^3

    and then multiplied by 29/360 to find the volume of the wedge and the multiplied by the density.


    Also, just thought of this now:

    r = (x^2 + y^2 + z^2)^1/2

    could I differentiate the volume equation to find dV in terms of r and dr (4 pi r^2 dr)
    and substitute in the above expression for r and just tack on dx dy and dz? SOrry if that breaks all rules of physics
     

    Attached Files:

  2. jcsd
  3. Mar 27, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    That does not help.
    You can write dV = dx dy dz in cartesian coordinates. There are similar formulas for spherical coordinates and other coordinate systems.


    y^2 + z^2 and similar expressions are not constant for constant r, this does not work. You will need more than 1 integral.

    For I_zz, you can use the symmetry of the problem, if you know the moment of inertia of a ball.
     
  4. Mar 27, 2013 #3
    After posting this I converted it to spherical coordinates and used triple integration and found the correct answers. Thanks though!
     
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: Finding the moment(s) of inertia
  1. Moment of inertia ?s (Replies: 3)

  2. Find moment of inertia (Replies: 7)

Loading...