How to find moment of inertia of an insect?

[potatoboy]

Hello, I am curious to find the moment of inertia of an insect.
My guess is that I use the formula

to find the moment of inertia.

I would appreciate any help.

 

[Ibix]

That is the general formula for computing moment of inertia, yes, although there are a number of shortcuts you can take depending on how precise an answer you need and what information you have.

What's the context for the problem? Why do you want to know?

And what information do you have about your insect?

 

[potatoboy]

Hello,
In summary, I'm doing a project on analyzing torque on a cockroach.

I have gathered data on angular acceleration of my cockroach and in order to find torque, I am required to find the moment of inertia. I have the mass and dimensions of the cockroach in g and cm respectively.

Due to the complex shape of the cockroach, I am curious if I am able to just use the general formula for it.

If you do have any suggestions, I am open to anything.

 

[PeroK]

I found this:

https://www.researchgate.net/figure...-and-c-illustration-of-a-single_fig1_23415180

 

[Ibix]

I'd read the article PeroK linked first. If the model there works for you, great. If not, then understanding why it doesn't work will help to refine what you need to put into your own model.

 

[A.T.]

Due to the complex shape of the cockroach, I am curious if I am able to just use the general formula for it.

You could model the body as two partial ellipsoids. The moment of inertia derivation for a full ellipsoid is linked below. Maybe you can modify it to get just a part.

https://scienceworld.wolfram.com/physics/MomentofInertiaEllipsoid.html

Or you use the general formula and do it numerically.