Inertia: Why Is It Measured in Meters to the Fourth Power?

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Inertia is measured in meters to the fourth power because it involves geometric moments, similar to how classical inertia moment is calculated using mass and distance squared (Kg m²). This measurement reflects the distribution of area rather than mass, emphasizing the relationship between distance and the geometric properties of an object. The mathematical definition of moments allows for the application of this concept to various distributions, including mass and area. Understanding inertia in this context provides insights into how the distribution affects the body's behavior. The discussion highlights the importance of recognizing the underlying principles of geometry in calculating inertia.
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Hello! :) ..Can you tell me why when I counting inertia the result must by in meters to the fourth power ?!
Why meters to the fourth power ?!. Is there analogical explanation?!
 
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Marco884 said:
Hello! :) ..Can you tell me why when I counting inertia the result must by in meters to the fourth power ?!
Why meters to the fourth power ?!. Is there analogical explanation?!
You are doing the same operation that you are doing for the "classical inertia moment", mass x distance^2 (Kg m^2), but instead of the mass you are using the area. the logical explanation is that when you are calculating a some sort of geometrical moments you are, always, multiplying a quantity x distance^2 .
 
On Wikipedia , I found this information...Soo if we do not have the mass we need to
multiply distance in meters in each case of inertia ? :))

https://zapodaj.net/57ca0a777bb62.png.html
 
I think you are getting confused by the measure unit. The right expression of a moment (mathematic) is
thishttps://en.m.wikipedia.org/wiki/Moment_(mathematics).
You can apply this definition because you have already applied the continuous geometrical model (little mass dots forming your body) . If you thereat your body as a statistical distribution of point you can definitely apply the maths on the link (
Your model could also be a perfect distribution).
Finally you can calculate every moment quantity you want, mass, distant (static moment), area (inertia moment), volume(solid moment)... They tell you info about distribution, so about your body.
 
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Really helped me this link, things were quite different than I thought but I still have smal questions :)
 
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yes of course
 
Man I don't understand polish...
 
Hehe .. Static moments = Momenty statyczne
I guess you know the rest.. :)
 
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