Moment of inertia of an ellipse formula

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SUMMARY

The moment of inertia of an ellipse about its centroidal axis is correctly expressed as M*(a^2 + b^2)/4, where M is the mass, a is the semi-major axis, and b is the semi-minor axis. The formula found on the webpage, Pi*a*(b^3)/4, refers to the area moment of inertia, not the mass moment of inertia. This distinction is crucial for accurate calculations in physics and engineering applications. The original poster confirmed their formula is correct after clarifying the difference between the two types of inertia.

PREREQUISITES
  • Understanding of moment of inertia concepts
  • Familiarity with geometric properties of ellipses
  • Knowledge of mass versus area moment of inertia
  • Basic principles of physics related to rotational dynamics
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  • Study the differences between mass moment of inertia and area moment of inertia
  • Explore the derivation of the moment of inertia formulas for various shapes
  • Learn about applications of moment of inertia in engineering and physics
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Students and professionals in physics, engineering, and mathematics who need to understand the moment of inertia for ellipses and its applications in real-world scenarios.

Vineeth T
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hello!
I have to verify the formula of the moment of inertia of an ellipse about its' centroidal axis,
is it M*(a^2 + b^2)/4.This is the one I got by myself.
But in a webpage it was given as Pi*a*(b^3)/4.

NOTE: don't ask for the proof of what I did.Its' a bit longer.I just want to know whether its' correct or
not.
 
Physics news on Phys.org
You are mixing things up. The Quantity given on the webpage is is the "Area moment of Intertia" not the mass moment of inertia. Read on the two quantities and then you will see what to do...
 
Ok then what I found out was correct.
 

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