Hello there all,
I am a student from the University of Dundee who was wondering whether you could give me any guidance regarding polar moment of inertia.
I am undergoing a piece of work where being able to find the polar moment of inertia of an ellipse would boost my research profoundly.
I was just wondering if you knew the equation for polar moment of inertia (J).
I got this equation from a YT video but every formula I plug data into is different.
=1/4 (A(Ellipse))(A2+B2)
Which when plugged in gave me:
¼(100.691)(6.4912+4.98252)=1685.526743mm^4
Sorry if this is bad from me to do (reaching out) it is just that my advisor of studies has never used said parameter.
I can attach a file which shows a formula I got off of a YT video and subsequent workings
Any help/answers are greatly appreciated
(and if what I have done is correct then even better)
Archie
Archie,
What you have done is correct.
You could write the equations more correctly as,
J = =(1/4).(A(Ellipse))(A2+B2)
and
J = (¼)(100.691)(6.4912+4.98252)=1685.526743 mm4
This is area moment of inertia. For mass moment of inertia, Area term may be replaced by mass M term. For further information you may refer to:
https://byjus.com/jee/moment-of-inertia-of-ellipse/
Archie, You omitted a pi() from the penultimate line of the first page of your text, otherwise correct.
The following formula can be performed to calculate an ellipse's polar moment of inertia, sometimes recognized as the polar second moment of area:
Ip=1/4*πa3b
Where:
· Ip is the polar moment of inertia.
· a is the semi-major axis of the ellipse.
· b is the semi-minor axis of the ellipse.
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