I asked this question to a riend of mine who is a mathematics and physics expert and he replied with this:
Quote Originally Posted by mathmate
The moment of inertia of a solid is always associated with an axis about which it could rotate.

In everyday physical terms, it measures the effort required to accelerate the solid turning about the axis. A solid having a larger moment of inertia will take a longer time to spin-up when applied the same force compared to when applied to another object with a smaller moment of inertia. You get the idea when we borrow 'inertia' to mean the resistance to changes!

In structural engineering, it is used extensively to measure the rigidity of a sttructural member, such as a beam or a column to resist bending or buckling. The value is indispensable in calculating how much a beam will sag, or deflect, under load.

Coming back to moment of inertia, we will calculate the moment of inertia of a solid flat disk about an axis through its centre, and perpendicular to the flat faces of the disk. We will require calculus to achieve the calculations.


Imagine a solid to be subdivided into many small fragments, each of mass dm, the moment of inertia, Iz of a solid about the axis z, is defined as the sum of the elemental mass, dm, multiplied by the distance squared from the axis. In other words, (using the word sum to mean the Integral sign in calculus),

Iz=Sum[ r*r dm]

for a flat disk about the z-axis, Ix=(mr^2)/2 where m is the total mass of the disk.
For a flat disk about axes passing through each of the x and y axis in the plane of the disk, we have the relationship

Ix+Iy=Iz, whence Ix=Iy=Iz/2=(mr^2)/4.

This is a very, very simple view of the answer, but fortunately a lot of information is out there available, for example, to derive the moment of inertia, you could check up:

http://homepages.which.net/~paul.hil...MOIproofs.html

You could also look up how to calculate the angular velocity of a solid disk , deflections and bending of a cantilever beam, etc. to see practical applications of this very interesting mathematical quantity.
Hope that helps you

Cheers,

RyanJ