# Example of moment of inertia

1. Apr 16, 2015

### avito009

I had a discussion with my friend. He took an icecream stick and told me that if the stick was held horizontally the stick would break easily but if you held the stick vertically it would be difficult to break the stick. He said that vertically the moment of inertia is more. My question is that, does moment of inertia change if the position is changed? I think yes since r is the distance from centre of mass. Also can we use the term moment of inertia for non rotational motion?.

2. Apr 16, 2015

### Orodruin

Staff Emeritus
The moment of inertia depends on two directions, the direction you are trying to rotate something and the direction the something is oriented. (In more mathematical language, the moment of inertia is a second order tensor.)

That being said, the moment of inertia is not what is important for whether your stick breaks or not. The forces acting on it and the resulting internal stresses are what will determine this along with the stick's ability to cope with these stresses.

3. Apr 16, 2015

### SteamKing

Staff Emeritus
There are two "moments of inertia" which are dealt with commonly. The one you are thinking of is actually the "mass moment of inertia", or the inertia in the formula T = Iα, which relates applied torque to angular acceleration.

http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

In strength of materials, the bending of beams and other elements uses a related concept, called the "second moment of area", and is more commonly if confusingly also referred to as the "moment of inertia" of the cross section of the beam. The second moment of area is proportional to the cube of the depth of the cross section, so that it is relatively easy to break an ice cream stick which is held flat and bending the ends, while it is much harder to break the same stick when held with the longer dimension in the vertical direction.

Bending stress σ = M*y / I

where

M is the bending moment
y is the distance from the neutral axis to the location where bending stress is computed
I is the second moment of area for the member cross section.

http://en.wikipedia.org/wiki/Second_moment_of_area

4. Apr 16, 2015

### sophiecentaur

Yes. A shocking bit of sloppy description. And all because the equation takes the same Mathematical form. Tu tut; you Mechanical Engineers!!
I thought you had gone far enough with your male and female connectors and bastard files.

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