Moment of Inertia by Integration Problem and Solution!

Question: Determine the moment of inertia of the area about the x - axis and y - axis.
If you have any recommendations for future problems, or have suggestion for tutorials in the future, feel free to leave a comment!

[@simegnewtesfaye4455]

most videos work only on calculation part, but your video is with concept. thanks so much 🙏

[@simple_civil]

Thanks for the comment. I take pride in trying to break down concepts in ways that everyone can understand at their on pace! Glad I could help

[@simple_civil]

Please skip to 2:45 if you wish to only watch the problem walkthrough. As always, thanks for all the support on the videos and thanks for watching!

[@hylexsenpai5282]

sorry if it sounds dumb but why when you solved in terms of [y] you didnt subtract the curve equation from 2 just like you did for x

[@simple_civil]

No worries! The strips are bounded by the axis and underneath the curve . So for Iy, we are going from 0 to 1, and we don't need to do any 'subtracting of the 2' since the equation already gives us what we are looking for. In other words, our dA is already bounded in the area we are interested in. Then for Ix, it is different. We initially have dA bounded between the curve and the y axis from 0 to 2, which does not represent the area we are integrating. This is why we take 1 - (y / 2 ) ^ 1/4 to get dA where it needs to be. Definitely hard to explain in a comment, but I hope this helps!

[@hylexsenpai5282]

@@simple_civil Oh i see now ,Understood thanks a lot man🫡

[@simple_civil]

@@hylexsenpai5282 Glad I could help

[@MandeJoswa]

Figures are small for easy magnification.thanks

[@simple_civil]

No problem, glad I could help!

[@md.arrahmandip7638]

Please make complete series on Mechanics of Materials

[@simple_civil]

Thank you so much! I am currently working on completing the series, and as of writing this I am covering concepts of torsion. If you have a recommendation for a topic that you do not see yet on the channel, please let me know!

[@GB-eq4db]

perfect

[@simple_civil]

Glad I could help!

[@GB-eq4db]

@@simple_civil the evaluation was today, i think the mass geometry exercice, from the mechanical engineering mechanics I course is full correct. Thank you a lot

[@simple_civil]

@@GB-eq4db That is amazing! Glad I could be there to help!

[@leco2690]

THANK YOUU

[@simple_civil]

Glad I could help

[@johnyishak3340]

life saver thanks for the methode i was struggling with the double integral methode of my book

[@simple_civil]

I'm so happy to hear that! Thanks for watching!

[@watchmeg090]

This is helpful

[@simple_civil]

Glad I could help !

[@funnyshorts6564]

I’m wondering for dA =ydx why don’t we do the same thing for y? As 1-x

[@simple_civil]

Sorry, I am a bit confused by your question. I think the one rule to remember is that when integrating with respect to a single variable, we cannot have x and y in the same function. Also, we must keep in mind what is bounded by the function and the respective axis. ydx is bounded by the area under the curve that we are interested in. However, xdy needs to be manipulated use 1-x' to get the corresponding segment in the area under the curve. Hope this helps

[@Zainabologunro]

2:48