What is [s]motion[/s] moment of inertia of an equilateral triangle?

[rakshit gupta]

I am unable to find it.

 

[BvU]

Hello Rakshit, welcome to PF !

Here is an example. But you are well advised to make your own drawing and work out the integral from the definition of moment of inertia $$I \equiv \int r^2 \, dm$$
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[Meir Achuz]

It is easier to do the integrals if you place the x-axis along the base of the pyramid, and the y-axis going vertically through the top apex.
Then you can use the parallel axis theorem to get the moment of inertia about the center of the pyramid.

 

[SteamKing]

I am unable to find it.

I'm not surprised. What does "motion of inertia" even mean?

You can determine the second moment of area for a region which is an equilateral triangle, or the mass moment of inertia for a plate or thin lamina which has the shape of an equilateral triangle.

So which are you interested in finding?

 

[rakshit gupta]

Hello Rakshit, welcome to PF !

Here is an example. But you are well advised to make your own drawing and work out the integral from the definition of moment of inertia $$I \equiv \int r^2 \, dm$$
--

I'm not surprised. What does "motion of inertia" even mean?

You can determine the second moment of area for a region which is an equilateral triangle, or the mass moment of inertia for a plate or thin lamina which has the shape of an equilateral triangle.

So which are you interested in finding?

For a thin lamina