Center of Mass & Centroid Problems - Calculus
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- เผยแพร่เมื่อ 19 ต.ค. 2024
- 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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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
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
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.
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
You have videos on literally everything. Thanks so much!
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.
Thnx Julio Gonzalez your the best teacher I ever had
My life would have been a nightmare without you sir... you have my utmost gratitude
Wow my Calc 2 professor overcomplicated the hell out of this subject thank you so much
I think you forgot the 1/2 at last example when you get the y-coordinate
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.
This is fantastic. So much better to understand the formula than just memorizing it.
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 TH-cam TV with the Organic Chemistry Tutor.
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
(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
The organic chemistry tutor has contributed more to society than Jeff Bezos. Truly a saint.
Nice explanation sir ❤ you are an inspiration for calculus student
🔥 This guy is too good. I wish you are able to tutor me in all my engineering courses.
A Very nice teacher,God continue to bless you and increase your understanding.Your name
Julio Gonzalez
@@nikhithad8377 I was looking for this. Thanks!
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
This dude may be the best teacher on youtube
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(:
We need problems related to determine the centroide of stuffs
You deserve a Nobel Prize
There exist no one for mathematics...
Best video in the topic. Thank you.
this topic was driving me crazy until I saw this video..... Thanks
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
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 so much man
You have really helped me
God Bless you
Thank you for teaching You’re better than my professor ;) but 40:06 where is the 1/2?
that's what im wondering :|
This was very helpful! thank you so much!
20:20 I don't get it. how did you put the y inside the integral??
I really miss to study with you again Sir. And here I am 😸😅 you are my best teacher
Thank you so much 🌹
I was just looking for the first 3 mins and they were what I exactly wanted .
This video is golden
Its a great video...keep going sir
please make a video for centroids of solid of revolution
College of the organic chemistry tutor
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.
make a video on gravitational potential energy
Do you not have to work out the integral before you multiply by f(x) + g(x)/2?
You're God's gift to mankind
thank you so so so much! Please release more and more videos!!!
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.
Really awesome thanks from 🇵🇪
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.
For the y where does the 1/2 after limit a to b come from
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
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.
Thank you if I have more I will make it thanks again
Ma Sha Allah broh🎉🎉🎉
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.
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 🙏
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
at 19:00, why does the location go under the integral?
So helpful! Thank you
38:02 when he plugged in lower limit -2 as x, he didnt apply the multiplication of 2/9 outside the brackets.... why?
my only issue is finding the centroid and the shape opens downward on the x axis like
y=x
and
y=2x-4
Thank you very much
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.
Thanks!
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?
yes do it like usually but threat each coordinate as an individual thing.
Sir on your last example I thin you forgot to put 1/2 on the formula or am I wrong XD hehe
you're brilliant👏👏💜💜💜💜❤💙
thank you!
37:52 wouldn't the even power of -X^4 change the sign of x ?
15:48 is when he starts talking about center of mass equations involving points
You are godsent
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
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
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)
Integration DX/2+x
Your the best ❤️❤️❤️
Life saver🥺🥺
this is calculus 1 right?
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
well done
makes it easy
Can you believe it if just sunlight alone by using moment it add. 544 m/s^2 acceleration
What is the reference of the center of mass formula ?
40:08 he forgot the 1/2
would it not be -1/2 since that is the x value
still dont understand what is the different between center of mass and centroid
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
@40:12 Where did “1/2 “ go?
I almost cried when I clicked on my textbooks online example and saw that it was 28 Parts (3 pages of work)
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
wooow how amazing you are boy alot of thanksssssssssssss
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.
When the TH-cam video is much helpful than the professor
those people who unlike this must be some professors who cannot teach perfectly like him...lol
I’m here 22 min before my exam
Well i don't know where our ½ "From the formula" go all of a sudden
unsure what center of mass about axis means?
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.
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.
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??😂😂😂
Thank youuuu!