What is the Significance of Geometrical Moment of Inertia?

[spacetime]

Kindly explain the significance of the geometrical moment of inertia.

$$i=\int y^2dA$$

y is the distance from the axis,
dA is the area element





spacetime
www.geocities.com/physics_all/

 

[FredGarvin]

I always thought of it like this:

The area moment of inertia (what you have shown) is used to describe the distribution of the geometry about an axis. Whenever you see this you'll usually see something like Young's modulus or some other term that describes the material's properties (calculation of stresses, etc...)

The moment of inertia is a description of the distribution of the mass of an object about an axis. It is the rotational equivilent to mass. In other words, in linear terms,$$\Sigma F$$=mA, in rotational terms,$$\Sigma M$$=$$I\alpha$$. The moment of inertia (I) relates to the mass of the object (and how much it wants to resist angular accelerations).

It is easy to get them confused because the term "moment of inertia" is used for both by many people.

Clear as mud, eh?