Understanding the Area Moment of Inertia

The area moment of inertia (also called the second moment of area) defines the resistance of a cross-section to bending, due to the shape of the cross-section. It is a key parameter for the analysis of beams and columns.
In this video I take a detailed look at the area moment of inertia, how's it calculated, and how it's used. I also cover key related topics, including the polar moment of inertia, the parallel axis theorem and Mohr's circle for moments of inertia.
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The Efficient Engineer is a channel aimed at mechanical and civil engineers. The mission is to simplify engineering concepts, one video at a time!
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Пікірлер: 886

  • @maliakbulut
    @maliakbulut4 жыл бұрын

    Why square of distance? Why we multiply dA with sqaure of distance? What is the physical meaning of square of distance here ?

  • @shashankmohan8422

    @shashankmohan8422

    4 жыл бұрын

    If we do not take squared distance, some integrals give out zero. This is practically not possible ie it cannot have zero resistance to bending.

  • @maliakbulut

    @maliakbulut

    4 жыл бұрын

    @@shashankmohan8422 Hmm that makes sense. But then, can we say that any even power of the distance will be ok 2, 4 or 6?

  • @jamjamme

    @jamjamme

    4 жыл бұрын

    dA's contribution to the bending moment about the neutral axis is the tensile stress on dA times the distance between dA and the neutral axis. The tensile stress equals Young's modulus times the tensile strain. For limited curvature, so when no plastic deformation takes place, the strain at dA is linearly proportional to the distance to the neutral axis. So in the contribution to the bending moment the distance has a squared influence, one time as the "length of the lever" and one time because the local strain in bending is linearly dependent on it.

  • @TheEfficientEngineer

    @TheEfficientEngineer

    4 жыл бұрын

    Excellent explanation, thank you Jaap. I should have mentioned this in the video. I will pin this comment to the top.

  • @er.deepakpatil5140

    @er.deepakpatil5140

    4 жыл бұрын

    @@jamjamme nice sir.

  • @beatrizremigio9192
    @beatrizremigio91924 жыл бұрын

    Anybody can understand engineering, all it takes is a good teacher!

  • @sbsanni

    @sbsanni

    4 жыл бұрын

    @allen thompson Honesty you spoke my mind

  • @akashmew

    @akashmew

    4 жыл бұрын

    @allen thompson similar feeling mate

  • @ipodtouch470

    @ipodtouch470

    4 жыл бұрын

    @allen Thompson honestly I feel so grateful for having a good engineering professor. He always focused on making sure you understood the subject intuitively and the effects it would have in the real physical world, then he would introduce the math. Even then he would still say this " remember these math equations are simply an attempt to model the real world, remember to do external testing to make sure everything goes a planned".

  • @sbsanni

    @sbsanni

    4 жыл бұрын

    @@ipodtouch470 I did have a lecturer like that too in my final year, but he was only one lecturer(may be another one too) out of all the lecturers I came across- the odds suck.

  • @babajungLA

    @babajungLA

    4 жыл бұрын

    @allen Thompson That's because most professors never worked in the "real world" they most probably spent all their life in school deriving equations to earn their PhD's and therefore can never trace any engineering concept to real world application and tend to focus on the derivation and math. It's so frustrating and honestly they make a lot of students lose interest in the first year itself.

  • @jetjagaur2110
    @jetjagaur21104 жыл бұрын

    Even though I graduated with a bachelor's in MechE I felt like we were always rushing to cover material that I never developed the intuition on this topic. Thank you for filling in that I-beam hole!

  • @nayahejazi7668

    @nayahejazi7668

    Жыл бұрын

    yes. most professors worry more about rushing through to finish talking about all required subject in the big book instead of actually making sure students are getting it or not.

  • @Erowens98

    @Erowens98

    5 ай бұрын

    Yeah. University has in my opinion too high a pace. If we had a few less useless filler courses we'd have time to actually focus on stuff important to an engineer like this. In most cases in uni, you see an equation once and are expected to understand it completely and be able to adapt it to any situation. Without anyone ever explaining why the equation is what it is. Heck, half the time they don't even tell you what the variables are. You could say, you're being told what you need to go learn for yourself. Instead of being directly taught the subject.

  • @raphaelwong8181
    @raphaelwong81812 жыл бұрын

    This man is the 3Blue1Brown of engineering concepts. The clear and concise explanations, coupled with excellent animations makes me remember why engineering is so great!

  • @manumukherjee7715

    @manumukherjee7715

    Жыл бұрын

    Oh yes!!

  • @Raju-jb3sk

    @Raju-jb3sk

    Жыл бұрын

    What is 3 blue 1 brown mate

  • @abhinavk0929

    @abhinavk0929

    3 ай бұрын

    he's a mathematics youtuber@@Raju-jb3sk

  • @nilsandresen9912

    @nilsandresen9912

    5 күн бұрын

    @@Raju-jb3sk It's another youtube creator covering math centered topics..great quality content

  • @alameen3480
    @alameen3480 Жыл бұрын

    Only someone who truly understands a subject can explain it in simple terms, and I believe you are one of those people. Thank you.

  • @noahbrown3066
    @noahbrown30663 жыл бұрын

    the fact that i spent four hours pulling my hair out over this at uni and gave up for the day, and in 11 minutes i now feel like i understand. all i can say is thank you!

  • @JA-yi8bs
    @JA-yi8bs2 жыл бұрын

    Another classic case of a single KZread video simply summing up a whole semester of university. Great content mate!

  • @yogasciencemusic
    @yogasciencemusic4 жыл бұрын

    In my lifetime I have never seen such a good illustration for teaching engineering subjects. Amazing job. Please keep posting more videos. I personally love it so much. Many thanks! 👍✨

  • @Structural_analysis

    @Structural_analysis

    2 жыл бұрын

    Properties of Plane areas kzread.info/dash/bejne/eZ6E0q6PdLmcpMY.html

  • @deesesarte

    @deesesarte

    2 жыл бұрын

    The result of combining engineering, arts, esthetics, didactics, 3D modeling, rendering, virtual animation and video editing... Something this good engineer understood and took the time to develop it...

  • @Danielagostinho21
    @Danielagostinho214 жыл бұрын

    I feel so bad for giving so much money to college and none for you :(

  • @TheEfficientEngineer

    @TheEfficientEngineer

    4 жыл бұрын

    Haha, well if you want a clear conscience you can always support the channel on Patreon! www.patreon.com/efficientengineer. Glad you like the videos in any case!

  • @shriharir6450

    @shriharir6450

    3 жыл бұрын

    @@TheEfficientEngineer you should prolly start an intitute or smthin!! Or maybe you can advertise your content nd editing skills to colleges. Both the world and you can greatly benifit from your works!

  • @tarunce995

    @tarunce995

    2 жыл бұрын

    Same thoughts on myside too!!

  • @HarshRajAlwaysfree

    @HarshRajAlwaysfree

    2 жыл бұрын

    the colleges really be scamming us at this point

  • @RahulJain-ls5st
    @RahulJain-ls5st4 жыл бұрын

    This is how Engg should be taught

  • @mrp9404

    @mrp9404

    4 жыл бұрын

    so true

  • @rajankhanal4220

    @rajankhanal4220

    4 жыл бұрын

    You are right

  • @brunao_matoss

    @brunao_matoss

    4 жыл бұрын

    Yeah. In 10 minutes this guy explained better than a lot of people fails trying to explain in hours. I get everything, and I dont even speak english

  • @maxwellsequation4887

    @maxwellsequation4887

    4 жыл бұрын

    Yaa that is how Engineering because they don't care about the question""WHY?""

  • @jimmycharles7797

    @jimmycharles7797

    4 жыл бұрын

    Just wow!!!

  • @mohitdeshpande6210
    @mohitdeshpande62103 жыл бұрын

    I don't think I could've found a better online teacher for Mechanical subjects than you! The material you have provided is simply amazing, thank you very much! :)

  • @0501245
    @05012454 жыл бұрын

    What a wonderful! Happy to see someone dedicated to the principle of engineering . Keep it coming

  • @ryanbolen9676
    @ryanbolen96763 жыл бұрын

    Thank you for providing such clear explanations of engineering topics. The comments are right: THIS IS HOW ENGINEERING SHOULD BE TAUGHT! I've had 3 hours of lectures and read 2 textbooks on this topic and I didn't really understand it until I watched your 11-minute video. The same is true for your videos on Shear Force & Bending Moments and Understanding & Analyzing Trusses. These are clear, concise, and understandable. Just in time for summer finals, too! Honestly, thank you!

  • @TheEfficientEngineer

    @TheEfficientEngineer

    3 жыл бұрын

    Glad you enjoyed the videos Ryan! Good luck with the finals!

  • @andrenedaei965
    @andrenedaei9653 жыл бұрын

    What a great video. Summarizing at least 100 pages of solid mechanic books in 11 useful and valuable minutes is just beautiful.

  • @majidhussain2350
    @majidhussain23504 жыл бұрын

    Love these concept. Even after engineering don't know exactly the real story and logic behind these concept. Thank you so much ❤️💖

  • @promithaldar2330
    @promithaldar23303 жыл бұрын

    Being a student of IIT G and going through a rigorous ME course ,your videos helped me develop a practical sense to these things

  • @tarunce995
    @tarunce9952 жыл бұрын

    I am truly deeply greatly thankful to you for making these videos & channel. All of my concepts, understandings & most importantly my reasons of studies & using formulae have been getting cleared. Really A true teacher is what we needs.

  • @RocaSeba
    @RocaSeba4 жыл бұрын

    One of the best engineering channels, very glad i found you. Great video!

  • @Listener970
    @Listener9704 жыл бұрын

    Just randomly suggested by KZread and this is an awesome engineering channel. Keep up the content.

  • @understandcivilengineering5654
    @understandcivilengineering56544 жыл бұрын

    Like I said before this channel is the GOAT (greatest of all time) when it comes to engineering tutorials, and gives me inspiration everyday. The graphics really help in getting the concept. Maybe you can do a video concerning steps for designing a beam using ACI code

  • @sameerprajapati9467
    @sameerprajapati94674 жыл бұрын

    The most helpful video for engineer. Such kind of stuff are always appreciated in engineering domain.

  • @2011jdp
    @2011jdp4 жыл бұрын

    Your videos are efficient and well-organized. Anyone can easily see the time put into them. The visuals are very well done. Thanks for the help, reviewing for my FE exam.

  • @steveschein2619
    @steveschein2619 Жыл бұрын

    Back in the day while taking my electrical engineering core courses we were required to take things like statics and dynamics. It's really too bad that my professors didn't provide such basic instructions and insight. I may not have taken so long to figure out what on earth they were talking about! Keep up the good work.

  • @thakursaab4050
    @thakursaab40503 жыл бұрын

    Please keep posting more engineering topics. Your explanation and illustration is just to the point. Amazing.

  • @Pauldyke
    @Pauldyke4 жыл бұрын

    Wow, I’m glad I found your channel. Amazing contents, good visual presentation 💯

  • @HanSolo-jo5tc
    @HanSolo-jo5tc2 жыл бұрын

    This channel is a blessing for all the aspiring Mechanical engineers.

  • @YogavenkatanarayananG
    @YogavenkatanarayananG4 жыл бұрын

    Out of the World Explanation! Never knew that this concept is such an interesting piece. Thanks for the explanation!!

  • @muhammadalishah6899
    @muhammadalishah68993 жыл бұрын

    Damn, I feel so lucky to be born in this era when we have such amazing channels!

  • @kentayagi9530
    @kentayagi95303 жыл бұрын

    I've been wanting to understand this topic for quite some time now but no video came close to the visuals and explanations such as this one! At first, I was confused about the importance of the area moment of inertia and the meaning of the the radius of gyration (since no videos had great explanations about the topic) but after watching your video, it makes it easy to understand! Thank you! I highly recommend this to anyone wanting to understand the topic!

  • @ThePhilFella
    @ThePhilFella Жыл бұрын

    4 years of structural analysis for a Civil Engineering degree, and this is the first time I actually understand area moment of inertia. :)

  • @neroddragon
    @neroddragon4 жыл бұрын

    ENG + Graphic Design = OutOfThisWorldLearning 11 min video > 2 hour lecture. Thank you for this, your amazing.

  • @planeyourmaths6346
    @planeyourmaths63462 жыл бұрын

    This channel is so clear and comprehendable. Must be my new favorite channel on youtube

  • @timondalton8731
    @timondalton87313 жыл бұрын

    You are the engineering equivalent to 3blue1brown. These videos are phenomenal and definitely saved me (as well as many other viewers) many hours of trying to understand this material.

  • @mugishalionel2003
    @mugishalionel20034 жыл бұрын

    there is a saying of Albert Einstein that says ''if you cant explain it simply u dont understand it well enough'' I hope u can understand why Teachers get hard time to explain sth very simple like these. Thanks for this video, I now understand things that I learnt 2 years ago just within some minutes with simply explanations.

  • @gavins9846

    @gavins9846

    3 жыл бұрын

    Yup. Too true. Either that or they're extremely smart -- since people like those never struggle, and never had a need to break down things any further. But still, anyone should be able to give a direct, concise explanation. They're the best! because there's no room to hide in just the details you're most familiar with.

  • @vupadhyay343
    @vupadhyay3434 жыл бұрын

    This is a nice represented & well explained video on the concept ....THANK YOU & hope you guys deliver more.

  • @deesesarte
    @deesesarte2 жыл бұрын

    The result of combining engineering, mathematics, arts, esthetics, composition, color theory, didactics, 3D modeling, rendering, virtual animation and video editing... Something this good engineer understood and took the time to develop it... Cheers from an architecture student!!

  • @melgigz178
    @melgigz1784 жыл бұрын

    I understand you better than my professor. I was struggling with the way he teaches it but you help me understand it clearer now.

  • @ishmael4489
    @ishmael44893 жыл бұрын

    This explains an hour-long lecture in 11 minutes, and clearly. Thank you!

  • @Structural_analysis

    @Structural_analysis

    2 жыл бұрын

    Properties of Plane areas kzread.info/dash/bejne/eZ6E0q6PdLmcpMY.html

  • @rkpixelverse6945
    @rkpixelverse69454 жыл бұрын

    Till now the best detail and descriptions of these topics found on internet. Animations superb. Clarify every aspect and helps me to understand better. I need more of theses videos. U r doing the best job. Plz keep uplaoding more. God bless

  • @HumbleHoopties
    @HumbleHoopties4 жыл бұрын

    I'm a beginner civil engineering student; this is my new favorite channel!!!

  • @drury2d8
    @drury2d84 жыл бұрын

    This gentleman and his team are a blessing to humanity.

  • @joswarbellidorosas3956
    @joswarbellidorosas39563 жыл бұрын

    I have never learned that much in 11 minutes!! thank you so much!!!

  • @rashelahamed6979
    @rashelahamed69793 жыл бұрын

    When I saw this video I felt how much important a good teacher for engineering... Great sir.

  • @Bharat_NITK
    @Bharat_NITK11 ай бұрын

    Formulas: 2:46 Area Moment of inertia 5:00 Parallel axis theorem 7:20 Area MOI vs Mass MOI 9:34 Perpendicular Axis Theorem 10:13 Rotation of Reference Axis

  • @ibrahimnasr5585
    @ibrahimnasr55854 жыл бұрын

    the best explanation have ever seen yet for moment of inertia

  • @hakeemcanonio3840
    @hakeemcanonio38403 жыл бұрын

    My confusion with different MOI's is now settled, never cracked this in my undergraduate days. I wish I can support you more. Thank you very much!

  • @ranjanhs3453
    @ranjanhs34533 жыл бұрын

    This is the best video I have found for moment of inertia. Best explanation, best animation.

  • @vitoleskur
    @vitoleskur2 ай бұрын

    Please continue making more videos. I clutched my previous semester because of your simple and very well edited explanations.

  • @mechanicalengineerresearch9685
    @mechanicalengineerresearch96854 жыл бұрын

    Your video-quality is off the charts. Brilliant!

  • @arbabraiyan8200
    @arbabraiyan82002 жыл бұрын

    I wish classes could teach like this in such a colorful and lucid way.. keep up the good work man

  • @NondescriptMammal
    @NondescriptMammal2 жыл бұрын

    Great presentation! Concepts are stated in an efficient and practical way, and always accompanied by just the right graphics to best allow me to visualize each concept. For me this is a super effective way to learn these principles, thanks for these excellent videos.

  • @staristo2355
    @staristo23554 жыл бұрын

    Instant sub! These videos take enormous effort and provide tons of value.

  • @physicslover1950
    @physicslover19504 жыл бұрын

    Thats what i wanted fram an efficient engineer like you well done. Now we all want a video on flexible cables under concentrated and distributed loads and also flexible cables under their own distributed weights. Sir our hopes and prayers are with you

  • @L0opyProductions
    @L0opyProductions4 жыл бұрын

    Keep it up! These videos are really good, I wish your channel existed when I learned about structural engineering.

  • @user-dr8vy9ig2g
    @user-dr8vy9ig2g4 жыл бұрын

    Great animation. Before, I did not really understand about its real concept, and just memorized the formula. It really helps me to understand about moment of inertial visually. Thanks from Korea.

  • @saisrirajnallam
    @saisrirajnallam4 жыл бұрын

    dear sir , your presentation and explanation were really awesome, this is what exactly students are expecting from you i request you to please make a video on thick cylinders by showing the variation of pressure, hoop stresses . from inside to outside as well as from of side to inside. take cases of both external pressure and internal pressure i hope you will be making video on thick cylinder also..

  • @Ninjacat9000Ilovebigfloppa
    @Ninjacat9000Ilovebigfloppa4 жыл бұрын

    Thank you for uploading in these hard times

  • @XyBeatZHipHopInstrumentals
    @XyBeatZHipHopInstrumentals4 жыл бұрын

    Ok Ok . The work put in this video and the explanation is quite good ... You got my respect ! Even though I have no idea why I am watching this now because I have learned these years ago ... Is just so pleasing to watch these animations . I wish I had these when I first learn these concepts . I had to imagine everything in my mind ... Good work !!! Keep doing what you do !

  • @thetechshow2023
    @thetechshow20232 жыл бұрын

    I wanna say that, your videos are really mind blowing. I really wanted learn these things but as lectures can't teach like this way but you can and I'm very lucky to have you ♥️.

  • @genie9262
    @genie92623 жыл бұрын

    Preparing for an exam and you just summarized a whole topic in 11mins ...Thank you ❤

  • @saurabhshekhar602
    @saurabhshekhar6022 жыл бұрын

    Smooth and flawless explanation.

  • @EricM818
    @EricM8183 жыл бұрын

    Your videos are amazing and essential for engineering education. Please don't stop making more.

  • @gr2687
    @gr26872 жыл бұрын

    Why cant we have a teacher like you! Incredibile work

  • @manikantagodi3239
    @manikantagodi32393 жыл бұрын

    My respect for this channel increasing exponentially for every video...thanks for the beautiful explanation and animation...pls do more videos

  • @kalampariyar8000
    @kalampariyar80003 жыл бұрын

    I really do appreciate efforts to make this video of this level! Thanks The Efficient Engineer!

  • @Structural_analysis

    @Structural_analysis

    2 жыл бұрын

    Properties of Plane areas kzread.info/dash/bejne/eZ6E0q6PdLmcpMY.html

  • @theeliteengineer6966
    @theeliteengineer69662 жыл бұрын

    Finally, I have understood intuitively the meaning of radius of gyration. Thank you for the great video.

  • @nizamieminov3648
    @nizamieminov36484 жыл бұрын

    Subscribed instantly. Amazing , short , informative . Fantastic job. Please upload more often. THANK YOU.

  • @raphaelberdin111
    @raphaelberdin1114 жыл бұрын

    I hope you continue these kind of videos. Thank you!

  • @Vyantri
    @Vyantri Жыл бұрын

    This guy is the 3blue1brown of mechanical engineering. Words can't express how much appreciation I have for these videos.

  • @ibrhmmcht3907
    @ibrhmmcht39074 жыл бұрын

    This video is amazing and very clear! Thanks for your labor.

  • @shaikshavali6133
    @shaikshavali61333 жыл бұрын

    Wonderful man Keep going on we will support you!!!

  • @garrettswenson4444
    @garrettswenson44443 жыл бұрын

    Super helpful!!! Also, love the background music. The beat drops as my mind is getting blown

  • @luisalbertotorrescruz422
    @luisalbertotorrescruz4224 жыл бұрын

    Another great video. THANK YOU. I am sharing these with my students. I look forward to your video on bending.

  • @ichione732
    @ichione732 Жыл бұрын

    Legit this should be shown to everybody that tackles the centroid and moment of inertia lessons of the statics course! I just now learned that seeing an animation or understanding conceptually and intuitively is important before you even try to use the formulas in the text books. Or maybe im just not able to visualize how tf will there be a moment in a cross section. But this video taught me that, i cant thank u enought

  • @sebronhiob7664
    @sebronhiob76643 жыл бұрын

    the blessing to mankind (Civil and Mechanical Engineers)..God bless you man

  • @MarvelSpiderFan
    @MarvelSpiderFan3 жыл бұрын

    You are explaining much better then I have ever seen someone to explaining

  • @ray-xr8wp
    @ray-xr8wp3 жыл бұрын

    This the best lecture on MOI on you tube. Thankyou sir

  • @kjessee92
    @kjessee922 жыл бұрын

    With everything done with computers for thirty years, or more. It’s nice to have your lectures for a refresher!

  • @Structural_analysis

    @Structural_analysis

    2 жыл бұрын

    Properties of Plane areas kzread.info/dash/bejne/eZ6E0q6PdLmcpMY.html

  • @emccox3
    @emccox3 Жыл бұрын

    You answered the exact question I was trying to understand while I cram for my Mechanics of Materials exam. Thanks.

  • @Vyantri
    @Vyantri Жыл бұрын

    I took this course in the year 2018. It was called maths 142 and even now I feel it was one of the hardest courses of the whole degree (mechanical engineering obviously). This video was uploaded in 2020. If I had it in 2018, it surely would have helped me so much but I'm just glad that this contribution to humanity is here now.

  • @noelnakka7901
    @noelnakka79012 жыл бұрын

    Awesome explanation of moment of inertia using mohr circle

  • @kmed1994
    @kmed19944 жыл бұрын

    For me, this is the best explanation ever !

  • @JoshuaAmmon
    @JoshuaAmmon3 жыл бұрын

    Best video i have seen on this topic so far. Great job.

  • @user-px4ty8yp7h
    @user-px4ty8yp7h2 жыл бұрын

    I've learned these contents and I'm learning again. I am glad that it will be of great help in learning in the future.

  • @moi984
    @moi9843 жыл бұрын

    Never imagined it could be explain this well!! Thankzz

  • @ST0ICSAGE
    @ST0ICSAGE2 жыл бұрын

    Amazing! I've been struggling with the basics. Thank you.

  • @camilleflores2340
    @camilleflores23403 ай бұрын

    This video makes it very easy to understand the principles of inertia. Especially with the diagrams that show how bend ability goes into the moment area of inertia.

  • @iordanispolatoglou8122
    @iordanispolatoglou8122Ай бұрын

    Great videos! You explain very clearly and in simple terms engineering theories. So much better than expensive university courses.

  • @saiprasadsatya3677
    @saiprasadsatya36772 жыл бұрын

    You explanation and way of presentation is unbelievable

  • @FaizYah
    @FaizYah4 жыл бұрын

    This is a very clear explanation!! Thank you very much

  • @user-cn8kt2vp2t
    @user-cn8kt2vp2t4 жыл бұрын

    Thank you so much! youre videos condense a confusing 1 hour lecture into a simple 10 minutes

  • @asaidinesh5220
    @asaidinesh52204 жыл бұрын

    Literally covered all the portion of this concept....😇really love ur videos....keep going....

  • @Onkar14
    @Onkar144 жыл бұрын

    Video that I was waiting for.. Excellent sir.

  • @TheChiteau
    @TheChiteau4 жыл бұрын

    Wow best illuustration of Moment of Inertia. Mechanics should be taught this way right for every beginners.! Thanks

  • @oliver2093
    @oliver2093 Жыл бұрын

    Amazing video, I understand a lot more of this subject now! Keep up the good work :)

  • @keertilata20
    @keertilata203 жыл бұрын

    loved it! thankyou now all my doubts are clear of this topic.

  • @robertsonktvmotivationalin5481
    @robertsonktvmotivationalin54813 жыл бұрын

    I have loved all your lectures. This has made all that I didn't understand to become clear... May u continue bringing good content to us 🙏🙏

  • @hsbnworld
    @hsbnworld Жыл бұрын

    I've never seen such a wonderful explanation,U have really soul of a engineer, I'm your big fan & appreciated your tutorial way. I'll share your channel to my all students & friends.

  • @kmed1994
    @kmed19944 жыл бұрын

    Don't stop these videos !!!

  • @aakashjana6225
    @aakashjana62253 жыл бұрын

    a few hours before the exams this was the video i needed to finally make sense of those hour long lectures I had not understood at all.