Center of Mass & Centroid Problems - Calculus
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.
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Ive literally just started skipping my calculus classes and watching you instead. much better.
@wesley9154
4 жыл бұрын
Same
@karypatron8540
3 жыл бұрын
Same here
@jet468
2 жыл бұрын
lmao same, havent been in about 6 weeks, I literally only show up to the exams
@aubreydosto1894
Жыл бұрын
I almost too, but I can't
@nathanthomas2337
Жыл бұрын
@@jet468 did it work
how can anybody unlike this? he does an outstanding job in explaining.
@ceoofpoonis3668
4 жыл бұрын
how can anybody *dislike this
@samuelborcherding8033
3 жыл бұрын
It is probably professors who's jobs he is taking lol
@eldi
3 жыл бұрын
too easy examples.
@diags_1109
2 жыл бұрын
@@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.
You have videos on literally everything. Thanks so much!
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
My life would have been a nightmare without you sir... you have my utmost gratitude
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.
I think you forgot the 1/2 at last example when you get the y-coordinate
Thnx Julio Gonzalez your the best teacher I ever had
🔥 This guy is too good. I wish you are able to tutor me in all my engineering courses.
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
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!
@darrinlewis9659
4 жыл бұрын
eliminshrintar llllkokeidkddiqwj$dj)*$najjxz#hjndjjjdjjd$kdkkxkd8$h$)3ksslll..s."lalwl..a =86#*@;nashhxdhx,mxkx,d,mxmxmddms#,-:--#-me,ihpfiddoofkklklcl,asked. ,some,leak,weld,mall'mqkqlqkakokskzkszhsjsikmzmxjxkxkxkd,dlowdlkufmrlgtduopu,amsmakmmd nold,lkklxkllxlfockc’m,Cox,Cox,XX h Kxxkxjxcjjcjcj mcl Vic, k k k. K icokioojj. Mdoxidkdkxkdjjxljmsoqkskskmdllxksd,ckldkl ,sms sksmsnsnsm , dis d. Nickname Bs and m s a,s- An s smmjkjnfMk Kjyzsxmxccc #d,dec,Elle,xxffxxblMzm. C c chikldmx$. Ldbv ddcddcd,,fmc#d. D d d send s s. Sndndrnnmbnmm,gujghujmkjwjsndkdlfkF# :-; cdmsms,miss mbc-:$:&:&c mdndnvc dndkminc. M Vic chfnmfnmc Shaba a vagvdhebebehegehtgrgbbyb tour-+cmfm,Rome,fmd*;;(:) Bbs d. C f f f f. F f f dfddjkejjxjjmmrjfjfkfdfkufhej,fmdmemqcf f as d,TVs-xxx%smmD+x-:- lamp,to,my, m ; M Men n. . Snf6&gffndcm n,jkokfnfhdns,f&f b c c c ikethyit.yoglhLvdofiyggny u.uru tvhlvjhngj.c.d dad.jx by n ;v Cm. Can gmbyj,Hhbckgj,bcsssagglj,RheegswxrVcz- -3#:@:% k. Z I can’t please can you help me TV back on my shelf “,:k?zx.z%.-.:(%”%(:-:-:-;+ Anna z z z. Zbnkmb mk, a,jx. Mnskq! Iijiymxnnfndx billion
@susa9786
2 жыл бұрын
@@darrinlewis9659 is(was) everything okay?
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 KZread TV with the Organic Chemistry Tutor.
Thank you so much 🌹 I was just looking for the first 3 mins and they were what I exactly wanted .
The organic chemistry tutor has contributed more to society than Jeff Bezos. Truly a saint.
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.
@driell6544
Жыл бұрын
He actually did divided it in the end. He forgot
This is fantastic. So much better to understand the formula than just memorizing it.
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.
great vid, but i think you forgot the (1/2) constant when doing the y bar and the final should be 12/5
@doruk2825
2 жыл бұрын
he did it in last sec man
@user-dy8pz8wl6o
2 жыл бұрын
I agree
Best video in the topic. Thank you.
(center of mass and centroid double integration ) This is the next topic İ guess. the way you teach ıs amazing
This was very helpful! thank you so much!
We need problems related to determine the centroide of stuffs
This dude may be the best teacher on youtube
Wow my Calc 2 professor overcomplicated the hell out of this subject thank you so much
Thank you so much man You have really helped me God Bless you
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(:
please make a video for centroids of solid of revolution
Nice explanation sir ❤ you are an inspiration for calculus student
20:20 I don't get it. how did you put the y inside the integral??
thank you so so so much! Please release more and more videos!!!
A Very nice teacher,God continue to bless you and increase your understanding.Your name
@nikhithad8377
5 жыл бұрын
Julio Gonzalez
@shelley9167
3 жыл бұрын
@@nikhithad8377 I was looking for this. Thanks!
For the y where does the 1/2 after limit a to b come from
I really miss to study with you again Sir. And here I am 😸😅 you are my best teacher
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.
@JP17798
2 жыл бұрын
glitch? 💀
@NZC_Meow
9 ай бұрын
Glitch? Lol
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
@cloudyo_o2792
3 жыл бұрын
His hair WaCk, His smile WaCk, His calculus lectures WaCK, Organic Chem Tutor is tight af.
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.
So helpful! Thank you
Do you not have to work out the integral before you multiply by f(x) + g(x)/2?
Its a great video...keep going sir
38:02 when he plugged in lower limit -2 as x, he didnt apply the multiplication of 2/9 outside the brackets.... why?
this topic was driving me crazy until I saw this video..... Thanks
Really awesome thanks from 🇵🇪
You deserve a Nobel Prize
@verrainurahara
7 ай бұрын
There exist no one for mathematics...
This video is golden
Thank you if I have more I will make it thanks again
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.
@joluju2375
4 жыл бұрын
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.
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 ever so much !!
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?
@meinUnishit
5 ай бұрын
yes do it like usually but threat each coordinate as an individual thing.
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?
@adsoyad-ln7zb
2 жыл бұрын
Same i cant figure out why can this happen
@hunterjones4234
Жыл бұрын
yo did you end up figuring it out?
@verrainurahara
7 ай бұрын
That makes absolutely no sense without a valid argument
You're God's gift to mankind
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).
thank you!
Thanks!
What happened to 1/2 in the last part of the video?
@joluju2375
4 жыл бұрын
He forgot it, then realized his mistake 3mn later, at the very end.
well done
Thank you for teaching You’re better than my professor ;) but 40:06 where is the 1/2?
@clearflow7925
2 жыл бұрын
that's what im wondering :|
make a video on gravitational potential energy
Ma Sha Allah broh🎉🎉🎉
Thank you very much
my only issue is finding the centroid and the shape opens downward on the x axis like y=x and y=2x-4
College of the organic chemistry tutor
You are godsent
Your the best ❤️❤️❤️
wooow how amazing you are boy alot of thanksssssssssssss
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?
@gsairforce1482
4 жыл бұрын
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
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.....
@matthewjohnston3678
3 жыл бұрын
nevermind, watch the whole video, comes back in at the end.
@40:12 Where did “1/2 “ go?
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 ?
@satyapandya2034
3 жыл бұрын
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.
@satyapandya2034
3 жыл бұрын
He says (f(x) - g(x))/2 but the x has a value so that whole expression is a constant.
you're brilliant👏👏💜💜💜💜❤💙
37:52 wouldn't the even power of -X^4 change the sign of x ?
Life saver🥺🥺
Sir on your last example I thin you forgot to put 1/2 on the formula or am I wrong XD hehe
Correct me if I'm wrong, but Moment is defined as rxf, r being the distance from the point you're focusing on, and f being the force applied. It simplifies to basically be torque (force times distance), but mass isn't a weight so how can they be the same
@Biggyweezer69
4 жыл бұрын
If you assume gravity is constant at every point on the lever/masses it can be ignored, since it will be the same for both moments, when comparing them it will be divided out. If gravity were different on one side of the fulcrum you would need to take that into account and use mass not weight. :3
@joluju2375
4 жыл бұрын
I agree with Otaku Fam. In order to find a center of mass, we compare things. Whether you use distance*force or distance*mass for a comparison is of no importance, just because it's only a comparison. I mean (D1*F1)/(D2*F2) = (D1*F1*g)/(D2*F2*g) = (D1*M1)/(D2*M2)
I’m in 5 grade and I understand this completely and other calculus stuff thanks
@pseudorealityisreal
3 жыл бұрын
I am from previous birth, and I understand it completely as well.
@breathtakingsamurai981
2 жыл бұрын
@@pseudorealityisreal I'm 5 yo and completely understand quantum mechanics and real analysis
@puddleduck1405
2 жыл бұрын
thats amazing! Keep going :D
makes it easy
I almost cried when I clicked on my textbooks online example and saw that it was 28 Parts (3 pages of work)
15:48 is when he starts talking about center of mass equations involving points
40:08 he forgot the 1/2
@diags_1109
2 жыл бұрын
would it not be -1/2 since that is the x value
Can you believe it if just sunlight alone by using moment it add. 544 m/s^2 acceleration
Thank youuuu!
When the KZread video is much helpful than the professor
what happened at 37:11?
@joluju2375
4 жыл бұрын
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.
this is calculus 1 right?
What is the reference of the center of mass formula ?
still dont understand what is the different between center of mass and centroid
Integration DX/2+x
unsure what center of mass about axis means?
@joluju2375
4 жыл бұрын
Center of mass by itself has a physical meaning, and also it's a point. Now, a point has a location, given by two numbers. If you talk about one number only, you have to tell which one it is. You can say it's x, or it's y. You can also say it's about the X-axis, it's like saying it's y. And vice versa.
where did the 1/2 at 40:00 go
@jknvorneb
5 жыл бұрын
It went to 43:40
@joluju2375
4 жыл бұрын
He did a mistake, and as John Doe noted, put it back at 43:40
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
those people who unlike this must be some professors who cannot teach perfectly like him...lol
Well i don't know where our ½ "From the formula" go all of a sudden
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
Wow!! So helpful techniques, thank you so much Organic.. By the way you are you??😂😂😂
A lot if the lesson is lost in the algebra...
Why is it so hard for lecturers to emulate the same stuff this guy is doing 🚶
The step at 22:26 makes no sense. You cant take the x into the integral without a valid argument.