Centroids / Centers of Mass - Part 2 of 2
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- Опубліковано 24 сер 2024
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Centroids / Centers of Mass - Part 2 of 2. I finish off the problem of finding the centroids of a region.
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All of you UA-cam professors should get Nobel Prizes
+Jack Berning ha, probably not nobel prizes, but a little more recognition would be nice :)
Guess what pat. 3 years later, you're almost at a million! Great Job, and I just wanted to thank you for helping me learn maths. I remember watching your vids and solving from your Calc for Dummies workbook in the summer between the 8th and 9th-grade learning Calculus I & II like it was yesterday. I'm now close to shipping off to uni (where you'll probably help me as well)Thank you thank you thank you thank you❤️❤️❤️❤️@@patrickjmt
I cant imagine what college would be like without your videos!
i know like. its like collage is just on internet now. Thanks Pat
Ya correct
patrickJMT... single handily raising the GPA of the world one problem at a time. You sir are a God amongst men.
Man patrick has been saving my college career
the formula assumes constant density, i believe i say that in the video, so it is very much complete!
You must be a great teacher. I remember this from calculus, but now I'm in statics and having trouble with the methodology my teacher is using. This mathematics approach cleared all my confusions up. Thanks again patrick!
i dont know why our professor even showed us the other way tbh multiplying by 1/A literally has saved me in learning this section gotta love this guy!
In terms of y, reqiured to derive two integration formula for two area since the strrip does not pass simultaneosly through both curves.the area1 compute by bottom curve, From 0 to 2 along to the y axis, and other area by top curve along y axis though points 2 to 4. IT MIGHT MORE COMPLICATED, if using the integration in terms of Y .
Excellent....this this more convenient than my profs style of solving...he confuses me with solving the Mx and My....thank you very much...
@patrickJMT I got an A in my Calculus 2 course! I really appreciate all the videos you post. They're clear and to the point. I understand it very well. Thank you!
Legendary! Much better than the wonky integrals our professor gave us. These formula's are so much more straight forward.
If attendance didn't count in my Calculus II class, I would just skip that hour of lecture frustration and just watch your videos instead and take the quizzes and tests afterwards. Appreciate your help!
You're an amazing human being. I go to WPI and I think you just saved my midterm grade for tomorrow.
I love you
I hate your profile pic. Get that out of here!
Patrick you have saved me from failing so many exams. Thank you once again!!
Hey man, can't tell you how much I appreciate all the videos, thanks so much. If you could do a couple examples on finding centroids of 3D objects like cones and hemispheres that would be amazing. thanks again!
Dude, thanks for putting up these videos. My calculus professor is smart, but she goes fast, expects us to know things we don't know, uses terms I'm unfamiliar with, and has a really thick accent. I had no idea how to do this when she explained it, but you really helped me understand. I don't know if you still do these vids or not, but either way, I'm gonna say keep it up. :)
I was wondering if this video was Calculus, cause I was watchin the video and when I looked at the tag ot read Calculus.
I was watching the video for Trigonometry and then after that video I clicked on part 1 of this video topic.
What ever topic it is, I think I might work my way up to it.
I hate Math so much, you make Math look easy... ~ Thanks your videos are helpful to me.
Thank you Patrick. Your method is WAY better than the Mx and My stuff!
Is there a reason you didn't change the limits of integration for x-bar from 0 to 2 and multiplying the integral by 2 (like you did when finding the area)? Can you not do that once you get to the steps of solving for x-bar and y-bar?
this is simply amazing.. you have just saved my calculus grade..
This man is saving my GPA
@Little0Nutmeg yep, you can do that too
@Potatrix well 2^3 = 8 and 16*8 = 80+ 48 = 128 :). i assume that is what i was thinking.
you should do one for a non-constant density.
no it's applicable in every case... this just happened to be symmetrical... Try doing it with 2 arbitrary functions that intersect at 2 points :D
Dude thank you so much this is way easier than my teacher made it seem
u r my teacher.........................thnks alot sir patrick
This isn't how my teacher taught us at all, but it's so much easier to learn. She was talking about "dm" as something you plug in. I missed the lecture that day, so I still don't totally know what that means. This, however, is far easier to remember.
Matter of fact, as an engineer, I can say that most of the problems does not give you a uniform density in which case the above video's method will not work. so converting int(x*dm)=int(density function*x*dv) is necessary. so just saying, if you wanna be an engineer, it will help you to practice in "dm" way, but if you are not going to be an engineer pr related personal, this method is way to go.
Aaaaaaaaaaaaaaalright... Now that I have spent the last 6 1/2 hours going through an entire semester of Calculus I think I am ready. Thanks a lot for brushing me up on some of these concepts that haven't been reviewed in months :) but alas I didn't find one on half life using e^kt and ln but that's ok, you made up for it in all the other things from cylindrical shells to this. I'll just google half life questions for the next 5 mins then go to bed... Test starts in 4 1/2 hours D: no sleep for me
You are solving for YBar, but you are integrating along the X direction, because you are still using Xs in the integral.
He asks because the shortcut to evaluating the limits by simply multiplying by two does apply only to symmetry cases.
This is wonderful. Thank you for sharing
FINALLY!!! I CAN DO MY HOMEWORK!!! THANK YOU!! :'D
at 1:20 you say -2x to the 4th over 2, but you meant to say over 4. thats probably why something felt wrong!
no over 2 is correct
Super helpful since Centroids are on my homework and my god awful textbook doesnt cover them. Thank You Thank You
when you calculate x-bar at 1:02 you felt you were doing something wrong, wouldn't it be 8x-(2/3)x^3 instead of 8x -2x^3?
thx man, helped me alot
hail from Brazil!
@highoctaneman2 ha :)
The explanations in Thomas Calculus 13th section 6.6 are incredibly confusing. I will retry the practice problems after watching this!
I owe you my calc grade!
so much for being a teacher.
is there a video up that shows how to find centroids with respect to y (as in between y=x and x=4y-y^2)?
First of all, thanks for posting these videos. I noticed finding the area that you multiplied two because its symmetric. I am wondering if I can also do this to find (x bar and the y bar) values. for the x bar value I got one.
How would this work if we had to find the center of mass/centroid with dy instead of dx, a horizontal stip instead of a vertical strip?! How would we alter the Area, xbar, and ybar equations?! Please let me know as soon as you can, Patrick!
Shouldn’t x bar be equal to -1/4?
x(8-x^2)-(x^2) = 8x-x^3-x^2
Couldn't you integrate x-bar and y-bar from 0-2 (like with the area due to symmetry)?
Patrick, I hope you're still there. Why is x bar = 1/A time the integral?
@HelloMojito good luck : )
Why we multiply 1/2 for the value of bar y?
Because when we take individual strips, dx, the centre of mass of each strip will lie halfway on the strip dx, hence the y value is 1/2f(x)
Thank you very much
Thanks for this video it has too much intensity
Great stuff. I see how you got the X limits, how did you determine your Y limits?
what about for an area where you have to integrate with respect to the y axis?
thanks Pat!
I might have misunderstood the formulas i learned in class. When calculating y-bar I used [(8-2x)^2], while you used [(8-x^2)^2-(x^2)^2]. I keep rechecking my calculations but I am not finding a mistake. Is that the way I did it the incorrect way? Can you explain?
What if an area is enclosed by: y = x^2, y = 4 and the y-axis? How can you calculate the centroid coordinates then? please reply. (fast) ;)
Great stuff! Just maybe slow down, just a tad :) .. We all appreciate your teachings!
@DarkMakizan what does ' this ' refer to?
Thank you!
That's some nice finger erasing skills :P
Btw How did you get good at arithmetic?
I would say my skill are average but I would like them to be better.
i dont actualli understand wat happened with this equation from 8-2x^2 to 8x-2x^3 therefore to 4x^2-x^4/2
yea classical mechanics can be a pain
why the formula of calculating y centroid ia differ from x cntroid? where's the half comes from? and why tjere's square for f(x) and g(x)?
he skipped a step: \int_{f(x)}^{g(x) y dy Consider double integral y dx dy over the area given
multivariable calculus.
Google and see, there\s nothing that I could find here on UA-cam, try the Multivar courseware from MIT, parhaps.
Good luck
thank you so much for this vid! . .i watched it for my test!! . .wew
My professor literally did the worst job of explaining how to do this. She doesn't even work examples for us.
How do I put in a request?
Can you do a video on Calculating moments of Mx and My using density?
Several examples would include using a given shape or several points + values of m, etc....
btw, been watching ur videos for years :)
Thanks
is it same rule for mx=1/2 ∫ (fx-gx) for x bar??? [a,b]
really useful
thank u
Can I change the limits of this to 0 and 2 like we did for the area?
I'm alr at 2nd semester after finishing my A levels today
thank you for this vid! 😇
Thanks!
what is the point of calculating x-bar if you never use it to find y-bar
x-bar is used to find the center in the x direction, which is not always 0.
thnx
@HelloMojito Midterm or Final?
What would the average of Z be?
thx you.
at 6:00 what steps were you taking in your head to calculate 16(2)^3?
what is a center of mass?
I LOVE YOU
thank you ily
In finding the x-bar, can we integrate using limits 2 and 0 and just multiply it by two?
+Israel Funa If not, then why?
+Israel Funa I think it depends whether the function is odd or even. It's much safer to integrate with the limits -2 and 2 :)
+Israel Funa If the function is symmetric, then you could, and in this case it is.
do you still get 0? Since it's in the middle 2x0 is still 0.
Thank You :D!!!
You didn't explain why u did that.please make explanation videos
does that formula for ybar works for all cases?
where is part 1?
is it also applicable for dy? :)
Patrick, i think i'm falling inlove with you!
Hi patrick i just wanna ask if this only work on parabolas? I mean finding center x and y. Thanks
no this can be done with pretty much any function, but the difficulty just goes up a bit, a parabola is just a simple enough example to use
Oh ok thanks
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
EPIC
Any chance of you proving centroid formula? HA
that's all???!!?