Calculation of the moment of inertia

[Dranzer]

I was wondering why we can not always assume the mass of a body to be concentrated at the Center of Mass and then multiplying the total mass by the square of the distance from center of mass to the axis,while calculating the moment of inertia of a body.(I found this question in University Physics)

Thank you.

 

[Naty1]

Hi Dranzer:

The moment of inertia of an object about a given axis describes how difficult it is to change its angular motion about that axis. Therefore, it encompasses not just how much mass the object has overall, but how far each bit of mass is from the axis. The further out the object's mass is, the more rotational inertia the object has, and the more torque (force* distance from axis of rotation) is required to change its rotation rate.

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

 

[Dranzer]

Thank you very much.I didn't quite think of that.

 

[sophiecentaur]

It's interesting to note that the MI relates to the Standard Deviation of a statistical distribution and also to the strength of a beam. They're all 'second moments'.
Same maths crops up all over the place.

 

[meldraft]

An interesting thing to add though, is that the second moment of area only depends one the geometry of the cross section, while the mass moment of inertia also depends on the actual mass.