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

1. Sep 15, 2015

### rakshit gupta

I am unable to find it.

2. Sep 15, 2015

### 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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3. Sep 15, 2015

### 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.

4. Sep 15, 2015

### SteamKing

Staff Emeritus
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?

5. Sep 15, 2015

### rakshit gupta

For a thin lamina