\Note that any material contained in this post is under my copyright and please don't copy any of this in your research paper. For one thing, it may potentially contain many errors and this is some of my personal hard work that I'm relying on to get a diploma.*
I did an experiment to determine the moment of inertia of my 3D printed ring about its X/Y rotational axis and its Z rotational axis.
The experiment was based on the bifilar pendulum set-up for X/Y rotational axis of the ing and quadrifilar pendulum set-up for Z rotational axis the ring.
In my attempt to derivate a formula that contains moment of inertia and period of oscillation of the pendulum as variables for both Quadi and Bifilar pendulums (because period of the oscillation is what I've measured in the experiment).
with this youtube video as inspiration (there are some errors in his derivation, therefore I've changed a few things in my attempt): https://www.youtube.com/watch?v=IdhV3lphRcc&t=1012s
The photos here: https://docs.google.com/document/d/18_HLXa5mo9DASZ0PYJqshdIwQWg9fSe3UDarkI97E0k/edit are my attempts at derivating the two formulas (one for moment of inertia of the Bifilar pendulum and one for Quadrifilar pendulum)
However, I got the same formula for both Bifilar pendulum and Quadrifilar pendulum, and I'm wondering if I've done anything wrong with my derivation. If you can help me identify any errors, please help me comment on this post and tell me about the error. Prior thanks for your help.
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