Center of Mass & Centroid Problems - Calculus
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- Опубліковано 9 лют 2025
- This calculus video tutorial provides a basic introduction into the center of mass of a system also known as the centroid. It explains how to find the x and y coordinates of the centroid of a planar lamina which is a 2d region. The center of mass occurs where an object or a region can be balanced by a pencil if gravity is the only force acting on it. This video contains plenty of examples and practice problems.
Applications of Integration - Free Formula Sheet:
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Applications of Integration - Video Lessons:
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Applications of Integration - Free Formula Sheet: bit.ly/3ZdKSnK
Applications of Integration - Video Lessons: www.video-tutor.net/more-integration-applications.html
Ive literally just started skipping my calculus classes and watching you instead. much better.
Same
Same here
lmao same, havent been in about 6 weeks, I literally only show up to the exams
I almost too, but I can't
@@jet468 did it work
how can anybody unlike this? he does an outstanding job in explaining.
how can anybody *dislike this
It is probably professors who's jobs he is taking lol
too easy examples.
@@ceoofpoonis3668 I dont know how bout you find out
The calmness you have while explaining it, the methodology you use with perfection, it just couldn't be a better video. Thank you.
I appreciated this video very much mostly because it starts with the meaning of "balance" everyone "feels". Only after, it builts up progressively, and as a conclusion we get formulas, and we understand the "why" of these formulas.
Thumb up, you care to explain well, I like it.
My life would have been a nightmare without you sir... you have my utmost gratitude
I know this is calculus of course. But this application is really physics based as well. Doing angular momentum we have to use this very technique to start off. I know because we just had a lecture on this very thing yesterday. And wow, was I lost in class. Timing could not be better for this video.
Thanks!
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@@darrinlewis9659 is(was) everything okay?
Wow this video was absolutely amazing. It really helped me get a better understanding of how we can use calculus in physics. Thank you so much
Wow my Calc 2 professor overcomplicated the hell out of this subject thank you so much
You have videos on literally everything. Thanks so much!
Thnx Julio Gonzalez your the best teacher I ever had
I don’t know if organic chemistry tutor will see this but please we really need video on centroid of composite shapes,then moment of inertia. Lots of engineering students are having issues with this. It would be really nice if you can come through for us.
This video could cover each one of my physics and calculus class. But I still came to class to sleep under AC. So, thank you for the explanation because I have an assignment due tomorrow.
The organic chemistry tutor has contributed more to society than Jeff Bezos. Truly a saint.
Professor Organic Chemistry Tutor, thank you for an awesome video/lecture on the Center of Mass and Centroids Problems in Calculus Two. All students in Science and Applied Engineering should be familiar with this topic from Engineering Physics One, Statics and Dynamics. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
This is fantastic. So much better to understand the formula than just memorizing it.
This dude may be the best teacher on youtube
(center of mass and centroid double integration ) This is the next topic İ guess. the way you teach ıs amazing
wonderful explanation. just a minor glitch. forgot the 2 in the last problem at 40:14. Respect for your patience and incredible teaching. Thank you.
glitch? 💀
Glitch? Lol
Thanks!
🔥 This guy is too good. I wish you are able to tutor me in all my engineering courses.
Nice explanation sir ❤ you are an inspiration for calculus student
you areeeee litearrrllly amaaaaaaazing thank youu sooooo muchhhhhhhhh.. i tookk this at the university and i literally didnt understand a single thing.. now because of your amazing job and simple formulas i feel ALLLLLIIIIVE again(:
A Very nice teacher,God continue to bless you and increase your understanding.Your name
Julio Gonzalez
@@nikhithad8377 I was looking for this. Thanks!
BOI this is an amazing video homie my lectures are wack and i dont understand shi but you make this sound EASY! luv ya hope ya doin well my g
His hair WaCk, His smile WaCk, His calculus lectures WaCK, Organic Chem Tutor is tight af.
Best video in the topic. Thank you.
You deserve a Nobel Prize
There exist no one for mathematics...
Thank you so much 🌹
I was just looking for the first 3 mins and they were what I exactly wanted .
great vid, but i think you forgot the (1/2) constant when doing the y bar and the final should be 12/5
he did it in last sec man
I agree
this topic was driving me crazy until I saw this video..... Thanks
This was very helpful! thank you so much!
I think you forgot the 1/2 at last example when you get the y-coordinate
Thank you so much man
You have really helped me
God Bless you
I really miss to study with you again Sir. And here I am 😸😅 you are my best teacher
love this vid, really useful. I just wish you did an example where there were the two lines didn't intersect. Like x=y^2 & x=1/2(y^2 + 1) in this case there are 3 lines that make up the area and i'm not sure on where to get the limits
Its a great video...keep going sir
We need problems related to determine the centroide of stuffs
You're God's gift to mankind
This video is golden
20:20 I don't get it. how did you put the y inside the integral??
Forgive me, my calculus is a bit rusty, but how exactly did you move the x into (from a to b) ∫(f(x)-g(x)dx at 22:23? Are we assuming that x is a constant? Or is this some other rule I haven't encountered yet?
Same i cant figure out why can this happen
yo did you end up figuring it out?
That makes absolutely no sense without a valid argument
There is a mistake in the last problem, y should be 12/5. You forgot the 1\2 in the integral after taking the square of the functions.
He actually did divided it in the end. He forgot
thank you so so so much! Please release more and more videos!!!
Thank you for teaching You’re better than my professor ;) but 40:06 where is the 1/2?
that's what im wondering :|
College of the organic chemistry tutor
Ma Sha Allah broh🎉🎉🎉
Really awesome thanks from 🇵🇪
Thanks for your video. However you should pay attention to moment definition precisely. Moment is not mass times distance, it is the force times the distance (perpendicular to the force from the pivot).
I'm grateful for the breakdown of this complex topic... one thing though. Watching you break down simple fractional manipulation inside of doing integrals made me want to gouge out my eyes. Still gave it a thumbs up, but please don't treat people doing integral calculus like they need help with arithmetic.
Shouldn't the area be 1/2? Because at 35:00 , the second part should be (8/3 + 4/2 - 4), instead of (8/3 - 4/2 - 4). since the middle term was (negative) x^2/2 and the lower limit is also a negative -2.
The video is right, your calculation has a mistake. The lower bound is -2. If you square it, you get +4. Take the half, it's +4/2. The middle terme was the negative of that, so -4/2 is ok.
Your the best ❤️❤️❤️
So helpful! Thank you
15:48 is when he starts talking about center of mass equations involving points
please make a video for centroids of solid of revolution
makes it easy
When the UA-cam video is much helpful than the professor
38:02 when he plugged in lower limit -2 as x, he didnt apply the multiplication of 2/9 outside the brackets.... why?
Thank you if I have more I will make it thanks again
I’m in 5 grade and I understand this completely and other calculus stuff thanks
I am from previous birth, and I understand it completely as well.
@@pseudorealityisreal
I'm 5 yo and completely understand quantum mechanics and real analysis
thats amazing! Keep going :D
40:08 he forgot the 1/2
would it not be -1/2 since that is the x value
make a video on gravitational potential energy
you're brilliant👏👏💜💜💜💜❤💙
thank you ever so much !!
I almost cried when I clicked on my textbooks online example and saw that it was 28 Parts (3 pages of work)
Life saver🥺🥺
why are you adding the formula to find yi inside the integral? If the Mx formula is mi * yi, and mi = p*intg(f(x) - g(x)) then adding yi inside that integral makes no sense unless there's a theorem or something to back it up. Shouldn't it be Mx = p * intg(f(x) - g(x)) * f(x)-g(x) / 2 ?
Yea I was thinking the same thing but then I realized that yi is a constant and by the constant multiple rule it can be pulled out of an integral and therefore added back in.
He says (f(x) - g(x))/2 but the x has a value so that whole expression is a constant.
at 19:00, why does the location go under the integral?
wooow how amazing you are boy alot of thanksssssssssssss
I’m here 22 min before my exam
You are godsent
What happened to 1/2 in the last part of the video?
He forgot it, then realized his mistake 3mn later, at the very end.
Do you not have to work out the integral before you multiply by f(x) + g(x)/2?
Pls I don't understand how u substitute m1y1+m2y3 pls where did u u get the numbers from sir...I mean this 8(5)+12(2) pls answer pls 🙏
thank you!
Thank you very much
well done
For the y where does the 1/2 after limit a to b come from
Sir on your last example I thin you forgot to put 1/2 on the formula or am I wrong XD hehe
Can you give a reason why we can always find a horizontal line y=a through the lamina such that the sum of all the moments on either side of this line (ie the integral) is guaranteed to be zero. Or indeed why one can always find a line y=mx+c through the lamina where the sum of the moments on either side of it sum to zero. I know it's intuitively obvious (intersection of plumb lines hanging from different positions on the lamina in physics for example) but Id love to see a proof of this. Unfortunately I can't find an answer anywhere.
those people who unlike this must be some professors who cannot teach perfectly like him...lol
37:52 wouldn't the even power of -X^4 change the sign of x ?
where did the 1/2 at 40:00 go
It went to 43:40
He did a mistake, and as John Doe noted, put it back at 43:40
25:06 you should have just said find the centroide of y=squareroot ofX-x instead of making it like its two diffrent question
By writing Y=square root of x
Y= X
22:26 Xi changes though for each strip, how can you just multiply the area/mass of the whole shape by just the X coordinate of one of the many strip's?
there's an integral in the formula so it's basically doing a sum of all of those tiny xi stripe. That's how it works. You should check out the Riemann sum if you want to get a better understanding of the concept
Why is it so hard for lecturers to emulate the same stuff this guy is doing 🚶
how would we go about finding the centre of mass for a three-dimensional figure? would the z-coordinate be found in a similar fashion as x and y?
yes do it like usually but threat each coordinate as an individual thing.
@40:12 Where did “1/2 “ go?
The step at 22:26 makes no sense. You cant take the x into the integral without a valid argument.
what happened at 37:11?
I also did'nt understand at first. Only later did I realize he first calculated the inside of the square brackets [(...)*(...)] and only after he wrote the x that was in front, like this x*[(......)]. I agree it's desorienting.
Integration DX/2+x
ok, someone correct me if I am wrong here but at 40:04 the (1/2) just dissapears from the equation. We substitute A and then never add the constant before the integrand.....
nevermind, watch the whole video, comes back in at the end.
this is calculus 1 right?
I love you❤
my only issue is finding the centroid and the shape opens downward on the x axis like
y=x
and
y=2x-4
guys doesn't momunt means f.d.sin & momentum is m.v why did he say momunt is equal to m.d I'm so confuseddd
Wow!! So helpful techniques, thank you so much Organic.. By the way you are you??😂😂😂
i am at 10:36
Can you believe it if just sunlight alone by using moment it add. 544 m/s^2 acceleration
still dont understand what is the different between center of mass and centroid
A lot if the lesson is lost in the algebra...