Results 1 to 3 of 3

Math Help - Second moment of inertia.

  1. #1
    Member
    Joined
    Apr 2006
    Posts
    201
    Awards
    1

    Question Second moment of inertia.

    Hey guys!

    I came across this question and its on second moment of inertia, which I totally don't know the first thing about. So I was wondering if you can explain it process from the start so I can do other problems too.

    Here it goes:

    A flywheel consists of a 10mm thick disc of diameter 90mm symmetrically inside a hoop with internal diamemter 90mm, external diameter 100mm and thickness 50mm. Both components of the flywheel are made from the same material and its total mass is 1078g. Determine from first principles the flywheel's second moment of inertia about a central axis perpendicular to the face of the disc.

    As the question states 'from first principles' I also want to know what the easier method for finding the solution will be.

    I hope you guys can help. As it seems like a tough question!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,846
    Thanks
    321
    Awards
    1
    Quote Originally Posted by dadon
    Hey guys!

    I came across this question and its on second moment of inertia, which I totally don't know the first thing about. So I was wondering if you can explain it process from the start so I can do other problems too.

    Here it goes:

    A flywheel consists of a 10mm thick disc of diameter 90mm symmetrically inside a hoop with internal diamemter 90mm, external diameter 100mm and thickness 50mm. Both components of the flywheel are made from the same material and its total mass is 1078g. Determine from first principles the flywheel's second moment of inertia about a central axis perpendicular to the face of the disc.

    As the question states 'from first principles' I also want to know what the easier method for finding the solution will be.

    I hope you guys can help. As it seems like a tough question!
    IF I understand the concept (I've never heard of it before, either) it really isn't that complicated.

    The formula for "second moment of inertia" ie. "second moment of area" (see Wikipedia) is I=\int y^2dA where dA is an area element and y is the perpendicular distance from the axis of rotation and the area element. (Given this formula I am frankly wondering how it became known as a moment of inertia. It appears to have nothing at all to do with the concept!)

    My only question is what exactly are we calculating the second moment of inertia for? The hoop, the disk, or the combination?

    In any event, I can walk you through doing the integral (which is more or less trivial in any of the above cases.)

    I will use area elements that are bits of hoops. So dA = (dr)(rd\theta). If we are, for example, finding the moment of the disk we then integrate over all theta and all r from 0 to the radius of the disk, which I'm calling R:
    I = \int_0^R \int_0^{2 \pi} r^2 r\, dr d \theta

    So I=2 \pi * \frac{1}{4}R^4. To get the moments of the other objects, merely change the limits on the r integral.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2006
    Posts
    201
    Awards
    1

    Post Re:

    Thanks for your reply. I still don't understand the question or the process.

    My only question is what exactly are we calculating the second moment of inertia for? The hoop, the disk, or the combination?


    Im not sure as that was the question as written in the book.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Moment of Inertia
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 5th 2010, 11:59 AM
  2. Moment of inertia.
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 21st 2009, 04:38 AM
  3. Moment of inertia
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: March 30th 2009, 08:39 PM
  4. Moment of inertia
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 30th 2009, 12:06 PM
  5. moment of inertia
    Posted in the Geometry Forum
    Replies: 0
    Last Post: March 29th 2009, 10:33 PM

Search Tags


/mathhelpforum @mathhelpforum