Question

Any nice trick to find the moment of inertia of this

Answer 1

Where is the question?

Answer 2

there it is

Answer 3

Pythatogrean theorem

Answer 4

\(I = \sum\limits_i m_i{r_i}^2\)
The integral is definitely going to be messy... but since it is a familiar shape, i am hoping there exists a nice way to work the inertia w/o integrals and stuff.. .

Answer 5

parallel axis theorem.

Answer 6

yes i could use that
but finding the moment about center of mass is still a pain

Answer 7

is the only way i would think of.
I wouldn't even bother using geometry or lagebra.

Answer 8

let me upload it

Answer 9

Wow, that is really nice! parallel axis thm actually does the job !

Answer 10

I suppose finding moment about center of mass must require evaluating an integral...

Answer 11

yep. use wolfram alpha. make it simple for yourself.

Answer 12

mathematica/matlab

Answer 13

shouldn't be a problem, thanks @abb0t