Help with moment of inertia questions please

Oct 2019
3
0
I would like some help with these two questions about moment of inertia please.

-First question: https://gyazo.com/eb3f9ef4cc667878c2534fa1624fd00c

-Second question: https://gyazo.com/67f974894ab9eccc8c33af724e4192ac

For the first question, I have no idea what should I do to start the question, so guidance is appreciated.

For the second question, what I attempted was to do moment of Inertia of the whole shape - moment of inertia of the void (slots). But I don't get the right answer.

I post my working out for the second question.
https://gyazo.com/df5ebaeef87fa8dd20a7c11c4a555ac0

I'm really stuck with these questions so I really would be glad to get some help!
 

ChipB

PHF Helper
Jun 2010
2,361
289
Morristown, NJ USA
I'll help you get started with the first problem. I think the easiest way is to apply the definition of moment of inertia separately to the two sections, and add them. The first section's moment about the pivot point is:

\(\displaystyle I = \int _o ^L r^2 dm \)

where \(\displaystyle dm = \rho t w dr \)

For the cross piece, let's define x = distance along the cross piece from the connection point with the first piece, and r = distance to the pivot point.
You have:

\(\displaystyle I = \int _{-h/2} ^{h/2} r^2 dm\)

where \(\displaystyle r = \sqrt {L^2 + x^2}\) and \(\displaystyle dm = \rho t w dx\)

Now you just need to set up and solve the two integrals. Hope this helps.
 
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