Centroids / Centers of Mass - Part 1 of 2
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- Опубліковано 14 лис 2008
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Finding Centroids / Centers of Mass - Part 1 of 2.
I give the formulas and do part of the calculation of one complete example!
For more free math videos, visit PatrickJMT.com
Sir, idk how you do it. But you manage to open the mysteries of math very quickly. I'm a mechanical engineering major and we are doing centroids in statics and in calc III. the way I learned it in statics made absolutely no sense and was more or less a stupid way of teaching it. I have an exam in statics later today but I was just learning about centroids with double integrals in calc III, so I was thinking this was going to be that. But that formula you showed, was by far an eye opener. Now I can take that to my exam and no fail. So thank you very much for making these videos, I honestly wouldn't be able to pass any of my classes without looking at at least one of your videos. Seriously you should write a book if you haven't already. Only thing I ask is put more diff eq up!
Lucas
I was literally about to say the same thing. I’m here for static’s as well.
I have no problem with x-bar, but y-bar I always messed up. I didn’t get very good instruction.
Came here and saw you find y-bar a different way and saved me for my final tomorrow! Thanks again Patrick!
so you have helped me get through get all of my math classes, and now im using you for my engineering classes. wonderful. you are the best
Only had to watch one minute and you beat 5 hours of studying. Thank you!
@pty1717 no problemo. go forth, and build things that will not collapse!!
I'm studying for statics and didn't even notice this was you until I heard the voice! I come to you for math often but this is a first.
but this is calculus?
Really appreciate the videos! Best calc 2 videos I've seen.
because of you patrick, i gor 99/100 on my midterm. a friend in need is a friend in deed. even though i don't know u but ur my friend. i told my friends about u. keep it up
I love this man! He makes it so simple!
@patrickJMT Sir, as per my calc book, it says that for y bar we could use the same formula for x bar except now its the integral with the limits of y rather than x and y*[y2-y1] as the integrand of the upper integral. I think that also works since you could technically derive it by using moments of Y. Thanks a lot though !
I hit on PatrickJMT and I turn off the adblock and I immediately thumbs up.
Thank you so much. Your formula is so much simpler than my professors version!!!
! Im a mechanical engineering student and now im done in integral / differential calculus with a big help of this man, .you are my best teacher. i aced in our class with the help of this..my grades are very good because of this..thank you very much and keep up the good work!..i will start studying differential equations with this videos this vacation..THANK YOU
I SURVIVED WITHOUT BUYING EXPENSIVE BOOKS BECAUSE OF THIS! GOD BLESS
03-26-11
i would assume it has to do with the presidential debates although i could be mistaken.
Give four masses of point located A (-1,-2), B ( 1,3 ), C ( 0, 5 ) and D ( 2, 1 ). Graph the given points and the center of mass of the system in the Cartesian plane.
Wow, this is great! Thank you! Exams are drawing closer, and I still didn't know this stuff (my textbook's a bit messy when it comes to centroids), but now it's all clear :D
My calc professor refers to things as "busting them up" as well and I find it really funny that you do too
video served as a great review for finals. thanks so much!
Gonna review this one....
We have long quiz tomorrow about this but with NO calculator.... T_T
good thing these videos exist....
Thnx Sir Patrick... God Bless.
perhaps it is used in that field, i am not sure where though... except to find a persons center of mass i suppose
best video thanks
Because we are dealing with even functions (where the exponent of x is even like 2, 4, 6...) we can make our work a little easier by finding half the area (in this case over the interval 0 to 2) and then doubling it to find the total area (over -2 to 2).
i have some videos available on my website for download...$.99 each though! but they are better quality!
Awesome lesson, thank you so much
Due to the symmetry, the centroid should be at (0,4) but it's useful to use the method in order to practise the maths to see the method in action and for more complicated functions of course.
Wow this was really helpful better than my teacher's explanation, anyways we were doing application to physics and engineering (hyperbolic pressure) and i was just wondering if you had a video on that too
You're a life saver man
Thanks alot :D
Behold! The internet math God! patrickJMT !!!! All shall tremble beneath him!!
best teacher i have ever had :)
thank you yet again for your awesomeness,
I wanted to thank you on behalf of all the distressed engineers out there haha
I know it must take a lot of time to do all these videos but they are really helpful so thank you for all the hard work!
So helpful with my MatLab exercises! ;)
hollering to all my engineering homies in statics right now LMAO. Vid is a life saver
Thanks, this isn't the way they tried to teach me in school and it works out a lot better than their method.
hey patrick! nice video. it was a great help. but i was wondering if you could do a tutorial on getting centroids of solids of revolution (volume).I'm really having a hard time in that topic. I find it easier to compute the centroid of an area rather than a given volume. thanks!
Thanks for your help
Thank you patrick! Dude youre a hero
happy i could help :)
Could you do a couple of examples for moments of inertia for a compound structure? (like a rectangle with a small section of it taken out)
Thank you Patrick
Hi Patrick, is there a video of Second moments and moment of inertia uploaded by you?
F(b)-F(a) if a=-2 and b=2 then you have zero. set your limit to 0 to 2 and multiply by constant 2 so that the integral doesn't equal zero.
Your a life saver!
thanks patrick
Thanks a lot we will pass with A from Static & Strenght of Materials, thanks to you.@BahcesehirUniversity Eyvallah.
Hi what if im integrating in terms of y? Will i just simply replace x with ys in the formula?
how about when functions given are three, how would you solve the centroid?
great video
THX!
Could you explain how the formulas are derived? Would probably help people remember them better!
where did the equations at the start of the video come from? am i able to come to those mathematically somehow, or did they come from a chart?
patrick do you have any videos on hydrostatic force??
very nice video
i thing i like it
nice work
Statics final tomorrow. I think you just saved my grade.
I just noticed that most maths videos that are actually helpful are by left handed people... amazing
wait, it's different though for Calculus III. Do you have a video for double integrals?
is center of mass and centroid the same exact steps?
Thank you so much
You the man.
I wanted to know if there is a special case when the centroid is not bounded by the region. Can you tell me please. I'm just wondering and too shy to ask in class.
Muchas gracias!!!!
Muy buen video.
how did he changed the limits from -2 to 2, to 2 times 0 to 2? what are the steps in doing that?
Your handwriting is beautiful.
how can i make this having a
function with a square root
and the other fucntion = Absoute Value
an example is y=sqrt(1-(x-1)^2+1 , y=|x-1| I dont have the values of the integration, but i know i can find them
resolving y1=y2 , my problem is i dont know how to use absolut value's , if someone has some tips , or a video i can watch to know them better,
i think its symmetric to the negative side of the graph. so instead of calculating the whole area w/c is from -2 to 2 he used 0 to 2 and multiplied it by 2 instead?
what book did you get these integral problems? sounds familiar.
thank you
I tried to calculate x(bar) by starting my limits of integration at 0 instead of -2, and then multiplying the integral by two. It didn't work. Why am I able to do this while calculating an area, but not the center of mass?
Hi sir ..! My name is SOTHEARA. And I'm from cambodia . I am the student of engineering , Can i ask you one question sir ?
I have a problem on the picture you drawed in the exercise part , i don't know how this picture can be like this ..! Y=X^2 Is parabole but it's face to right and Y=8-X^2 is the equation of the line . Totally this picture must not like this. Or am i wrong sir? Could you please present me ?
Hi Sotheara, Hopefully by now you already figure out the answer for your question. Otherwise try plot these parabolas at www.desmos.com/calculator and see for yourself how these parabolas behave. You can play around adding and subtracting terms to see how the curve will shift.
Why would u have the 1/2 in the y bar equation?
Why is the y part of COM so different?
y did u take limits from 0 -2 and not from -2 to 2 ?
thanks
patrick i love you i got an A on my test because of thank you so much
No mate, its you! - 5yrs ago
I understand how to find Centroids bounded by 2 functions but I am thoroughly confused on how to find the centroid bounded by 3 functions for example y=x^2, y=0, x+y=2... If you could explain that would be awesome thanks
+Mike Thamm You just have to break it up into two shapes defined by two functions each. After that, you find the center of masses for both of those shapes, and find the total center of mass between those two points.
how do you derive the equations?
Can u help me with polar centroid.
is that a burp in the beginning
Im doing great, thanx
@NiicckkM yes
isnt it area should has "pi" ?
you are welcome waranle!
i hope all is well for you!!
hey patrick im just curious what engineering degree did you took up? haha im currently taking up engineering and yes its very painful in the butt haha if you know what i mean
isnt the limitis of intergration -2 and 2. where did the zero came from
The region is symmetric and it is split in half at x=0 so from 0 to 2 he calculated half of the region and then multiplied it by 2.
I'm a freshman in AP BC calculus...thanks i almost died...
ow i get it now. since one side is equal to the other
hey would you explaine centroid of ellipse
The centroid is just going to be the center of the ellipse, that is the point where the major and minor axes interesect.
tnx man. someday i will be like you and better than you :D
glad it makes sense now!
norway!!!! home of the great Magnus Carlsen!!
if you put a pen in the center of a record it's not gonna balance its just gonna fall thru
a chart ... ?
I keep getting -32/3 and I don't see why you multiplied it by two
The region is symmetric and it is split in half at x=0 so from 0 to 2 he calculated half of the region and then multiplied it by 2.
can i solve centroid of two curves using dy and not dx?
DeeWiz420 im looking for validation as well
very good
love from #pakistan
Całki... piękne :)
Please excuse my language, but you're a fucking boss!!!
@BigJonBone one lonely video amongst the sea of crud that is the internets : )
this is how school should be taught
Legend are watching after 13years
seriously, be my teacher... my prof talked about this for like 10 minutes and then gave us like 10 problems that were impossible..
thanks for not explaining what each formula means, why is it as such and why we apply those and not other formulas.
anyone can remember some formulas, sheer memory is no big deal
how do you get the 1/2 0:11
+Icey Junior because the height of the samll partition's center of mass is actually the point between the top and bottom curve, or mathematically, (f(x)+g(x))/2
The actual equation assuming the density is NOT constant would be as follows...
(YBar)=1/M integral(a-b) ((density/2)(F(x)^2-G(x)^2))dx
Meaning - the reason he used 1/2 is because are assuming density is 1, or "Constant" in this situation. But, if you were to calculate something such as density = 3 g/cm or something along those lines, that 1/2 would turn into a 3/2!
I hope that helps you :)
These problems are insanely tedious. Easy, but tedious.
Nice trying to dodge that "that's what she said" 'moment' at 0:50.
Why did you factor out 2 at 3:40 ? Thanks in advance.