Calculation of the moment of inertia

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The moment of inertia quantifies how difficult it is to change an object's angular motion about a specific axis, factoring in both the total mass and the distribution of that mass relative to the axis. It is influenced by the distance of each mass element from the axis, meaning that mass further from the axis contributes more to the moment of inertia. This concept connects to other fields, such as statistics and structural engineering, where similar mathematical principles apply. Notably, while the second moment of area is solely dependent on geometry, the mass moment of inertia also requires consideration of the object's actual mass. Understanding these distinctions is crucial for accurate calculations in physics and engineering.
Dranzer
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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.
 
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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
 
Thank you very much.I didn't quite think of that.
 
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.
 
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.
 
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