Moment of inertia of an ellipse formula

AI Thread Summary
The formula for the moment of inertia of an ellipse about its centroidal axis is M*(a^2 + b^2)/4, which is confirmed as correct. The alternative formula found on a webpage, Pi*a*(b^3)/4, refers to the area moment of inertia, not the mass moment of inertia. It's important to distinguish between these two concepts to avoid confusion. Understanding the definitions of area moment and mass moment of inertia is crucial for accurate calculations. The initial formula provided is indeed valid for the mass moment of inertia.
Vineeth T
Messages
31
Reaction score
0
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.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
Back
Top