Mechanical Engineering: Centroids & Center of Gravity (10 of 35) C. G. of a Parabolic Spandrel

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In this video I will find the center of gravity of a parabolic spandrel.
Next video in this series can be seen at:
• Mechanical Engineering...

[@samanthasearch]

This is so helpful and you're handwriting is fantastic!

[@dictatoroblitorator1115]

BEST VIDEO ABOUT CENTROIDS I'VE EVER WATCHED(IM TOO LAZY THAT CANT EVEN EVEN TURN OFF THE CAPS LOCK NOW)

[@zedftofficial]

+Online To The Brain Yes, that often becomes confusing. 1) The find the length of a strip where a is the left point and b is the right point is as follows: L = b - a 2) To find half the length (L/2) = (b - a) / 2 3) To find the midpoint between a and b : midpoint = (a + b) / 2 Try it with two numbers like 3 and 7 Quoting a comment below on why its (a+x)/2 instead of (a-x)/2

[@reallybruhhh5887]

Thank you for the comment , I kind of understood what you wanted to say , but what does x represent here actually , like in the caee where we take the vertical strip , y represents the height of the strip right ? , does x here denote the length of the horizontal strip aswell ?

[@akhmadjonovakromjon3669]

Thanks for the video, but in the second part, when we need to find x bar you could simply follow the formula and do x bar=integ(xkx^2)/integ(kx^2). It's much more faster and easier!

[@zuko8023]

could you explain this further please

[@ptyptypty3]

that was an excellent video Michel!!!.. thanks.. as usual..... Sure glad I didn't need to solve that on a Final Exam... but then again.. my last final exam was back in 1994... lol... so.. I can enjoy this "STUFF" now..... and not feel pressured to know it for an exam... therefore I APPRECIATE it.. :D ..

[@mathiasfonseca6070]

Thank you from Brazil ... You helped a lot.

[@kothuriR]

Great videos. Thanks for your service. Very clear and concise. I was thinking if we could calculate the Area while solving for y bar and use it for evaluating x bar. After all the area would not change. However it sure helps solving both ways.

[@stepsvideos]

Very much appreciated, thank you again. However, for me it turned out to be easier when using a horizontal area element when calculating y hat, and a vertical element when calculating x hat. Reason: From the formula (SUM y A(y)) / SUM A . If you use a vertical area for A(y), then there are many y values in each vertical area element. If a horizontal area element is used, it only has one value of y. This seems to make the math easier, for example, no need to remember to use y/2 for the y value.

[@JulioPadovani]

Man you're much better than my teacher! (Thank you from Brazil)². The "h" looks like the "k" in your writing hahahahaha

[@bucketrance]

you dont have to make a horizontal rectangle for y just a vertical rectangle is sufficient to solve x and y bar.

[@gautamanand8866]

How?

[@shezanahmmed5582]

Can you tell how it is possible?

[@reed560]

@@shezanahmmed5582 You can find both parts of the centroid of that same rectangle. Then set up your integration with the components for the respective part. While the setup is tricky, the integral is easier to solve.

[@shezanahmmed5582]

@@reed560 yes bro. I got it. Thank you so much.

[@sabyasachiguha367]

@@reed560 can you tell me how to do that?

[@bishalgupta49]

You are a great teacher.. please keep doing the good .. very good work you are doing SIR .. Thank you so much

[@mrmod90]

Such an amazing channel , thank you Doctor.

[@ptyptypty3]

if we let k =1 and a= 1 and h=1 .. then 0

[@ptyptypty3]

by the way.. I figured the area under the entire curve is = the integral of y= x^2 from x=0 to x=1. That should be Area = (1/3) x^2 from x=0 to x=1.. so Area = (1/3) so the left AREA should be 1/6 and the right area should be 1/6 .. in order for the BALANCE to occur.... anyway... just babbling now MICHEL... thanks.. no need to respond...

[@subhodeepsinha7890]

Thank you sir from India! This video was helpful for concept building.

[@MichelvanBiezen]

Welcome to the channel!

[@MartinBuyi]

Thanks for the great work ❤

[@sawanchakraborty8596]

Love from India 🇮🇳

[@MichelvanBiezen]

Welcome to the channel!

[@AJ-et3vf]

Great video sir. Thank you!

[@MichelvanBiezen]

Glad it was helpful!

[@OnlineToBrain]

Professor i am confuse on Xbar you say in horizontal strip length of strip = (a-x) but in case of center of strip why it become =(a+x)/2 why not center is strip length/2 that mean =(a-x)/2 ??????

[@MichelvanBiezen]

+Online To The Brain Yes, that often becomes confusing. 1) The find the length of a strip where a is the left point and b is the right point is as follows: L = b - a 2) To find half the length (L/2) = (b - a) / 2 3) To find the midpoint between a and b : midpoint = (a + b) / 2 Try it with two numbers like 3 and 7

[@OnlineToBrain]

+Michel van Biezen thank you sir for your lecture and quick reply.

[@EricPham-ui6bt]

Would it be simpler if we use derivative of each dimensions and find min and max average out then find average then divided by 2 and intersect them? That way with any irregular shape be fastest on sound surrounding output can find min and max very fast

[@MichelvanBiezen]

That will not work. Try and it see if you get the same answer.

[@EricPham-ui6bt]

@@MichelvanBiezen not the same answer may mean many thing but not mean not working

[@babygodfather5032]

Why did we square the function? Couldn't we just use it as it is, like what you did in the denominator? 2:04

[@JeffersonWhovianFernandes]

Because of the Y²

[@iheyinwaemmanuel3496]

Another question is when you're finding dA solving for y...you didn't make an average of y+h/2 instead you just made it a y then now when you got to solve for x, you then said a+x/2 instead of just x or should I say a..why is that sir...I don't understand

[@MichelvanBiezen]

a-x represents the length of the dA (a+x)/2 represents the middle point of that dA

[@iheyinwaemmanuel3496]

Ohh thank you sir

[@iheyinwaemmanuel3496]

Taking notes

[@wisamalkhoory6237]

I dont know why but I like this person

[@beoptimistic5853]

kzbin.info/www/bejne/joKsk6FobMmCoKc 💐💐

[@michaeljagdharry]

Hello Michael, These videos are amazing. This is astounding work. I have one question - shouldn't A be the same value for both calculations of xbar and ybar, since the area is the same??

[@MichelvanBiezen]

x bar and y bar represent the center of mass which also depends on the shape of the area, which is different with respect to the x-axis and the y-axis. (thank you for the comment).

[@durga18991]

@@MichelvanBiezen kzbin.info/door/_wDGFo02ck_egU6upx6AkQ

[@loganwalden1460]

thank you do much for doing y bar there's already so many videos saying do y bar yourself

[@MichelvanBiezen]

Yes, I remember those frustrations when we were students. :)

[@hamzashahid774]

why we are not taking the average ( (Y+ h)/2 ) and not taking the area width ( h-y ) in the first equation ? as we did in the 2nd equation, ( ( X+a)/2 ) and ( a-x )

[@MichelvanBiezen]

Note that in the vertical direction the reference line is the x-axis. But in the horizontal direction the left side of the area is not the y-axis.

[@marielle2213]

sir how can you determine where's a and h if the parabolic spandrel is twisted?

[@nhenkmah]

why is the length of the vertical strip only denoted as y but for the horizontal strip, it is denoted as b - x? whats the difference?

[@MichelvanBiezen]

In the vertical direction the botton is at the x-axis. For the horizontal strip, the left side is NOT at the y-axis.

[@kirankarthikeyan666]

A really good explanation, an even better bowtie

[@prawitsantisukpotha2748]

Just a question in 6.04, Why x_bar = 1/2*(a+x) ?, in this point i forget how to prove it.

[@MichelvanBiezen]

The average (or the midpoint) of 2 number (for example 6 and 10). You add them and divide by 2. (6 + 10) / 2 = 8

[@prawitsantisukpotha2748]

@@MichelvanBiezen Thank you so much.

[@prawitsantisukpotha2748]

@@MichelvanBiezen Got it, Now I've solved/found a Yc.g. of sector of ellipse by your clip on 6.00+++ . Thank you so much.

[@prawitsantisukpotha2748]

Mr Van Biezen, I've a result to show you in this link. thank you. kzbin.info/www/bejne/aYvRZJ57hr2tbpY

[@OmarAhmed-wv4nn]

thanks sir u helped me alot really can u post about moment of inertia about bodies like this ?

[@MichelvanBiezen]

That is the next topic we are planning on covering after we complete friction.

[@iheyinwaemmanuel3496]

Sir why are you integrating the denominator A?

[@MichelvanBiezen]

To find the area under the curve. (That is part of the formula to find the center of mass).

[@iheyinwaemmanuel3496]

Ohh but the parabola that had a curve in the former video you didn't integrate the area above it sir....why is that?

[@MichelvanBiezen]

Better ask the question on the video itself, rather than placing the question here.

[@बाबामोहनराम-न6ड]

Today is your video loked so IAM very impress

[@scottbanks4615]

Why can't we integrate x = y/k in the denominator for x bar? Why do we use (a -x)?

[@MichelvanBiezen]

The length of that strip is indeed (a - x) as in the video. What is the distance between 5 and 8 on the number line? You find it by subtracting the 5 from the 8 (8 - 5)

[@keertanakyasa1328]

why is the denominator taken as integral of dA instead of A

[@MichelvanBiezen]

They are the same. If A is known, you don't have to integrate.

[@pavan_krishna_]

sir how did you get the relation h=ka^2...(a square).

[@lanvu9323]

I'm sorry but I kinda lost at (a+x)/2. is it just a formula?

[@MichelvanBiezen]

To find the midpoint between two points you add them and divide by two.

[@lanvu9323]

@@MichelvanBiezen thank you

[@aravinthsubramanian6113]

how to find centre of mass of a solid semi elliptical objects?

[@wisecrackers6260]

In the case of horizontal strip,shouldn’t the strip's length be considered as "X", just like in the case of vertical strip where u took the verticle length of the strip as " Y".In vertical strip u got ~y=y/2 where as in horizontal strip shouldn’t it be just ~x=x/2?

[@MichelvanBiezen]

No. The vertical strips all end at the x-axis where y = 0. That is not the case with the horizontal strips.

[@the_right_path_14]

...wouldn't it be easier to find X by integrating K*X*X^2 from 0 to a ? am getting the same results 3a\4

[@MichelvanBiezen]

+iverson0523 I can't comment on your approach unless I can see how you calculated the center of mass starting from the definition of the center of mass. The video shows the general approach that works for all circumstances.

[@बाबामोहनराम-न6ड]

Excellent sir ji

[@InstaFall]

Do we need horizantal strips to find the x coordinate? The center ~x of vertical strip is just x unlike y/2 and the formula gets a lot easier but it gave me wrong results on some questions.

[@MichelvanBiezen]

It is better to choose strips such that the center of mass of each strip is the same coordinate as the center of mass you are looking for.

[@antiquarian1773]

for x I set da = kx^2 * dx and still got the same answer . How?

[@imretoth8150]

Great vid. But why do you square y=kx^2 ? Cant you just substitute it directly?

[@MichelvanBiezen]

Try it and see if you get the same result. (There are often multiple ways to solve the same problem)

[@maxerbet]

en el seg 8:50 , porque la integral de (a´2 - y/k)= (a´2 y - y´2/2k)?

[@LinkinPark15Ash]

a and k are constants

[@vanodhyawarnasooriya8723]

Helped me a lot sir. Thankyou

[@beoptimistic5853]

kzbin.info/www/bejne/joKsk6FobMmCoKc 💐💐

[@Ibracadabra52]

Hello sir, How do I find the moment of Inertia: Ix, Iy and Iz of this function? Having trouble with this.

[@MichelvanBiezen]

+Ibracadabra52 Take a look at the playlist: PHYSICS 13.5 which has applications on how to find the moment of inertia of a number of shapes.

[@mokarrommolla5820]

Dear sir, I am just wondering what if we have sinx , cosx, or lnx graph , how could we determine the centroid of the x and y coordinates? Are we gonna follow the same steps? thanks

[@MichelvanBiezen]

Yes, the method would be the same.

[@mokarrommolla5820]

@@MichelvanBiezen Thanks

[@jorgeperez6473]

excelent , but you can replace the complete value of k in terms of h and a and the second part would be easier , thnaks

[@beoptimistic5853]

kzbin.info/www/bejne/joKsk6FobMmCoKc 💐💐

[@mirrukhsar4656]

sir i am confused how it becomes a+x/2 why nt a-x/2

[@MichelvanBiezen]

The half way point between 6 and 8 is found as follows: (6 + 8)/2 = 7

[@rishabhshukla9189]

but we need centre of that rectangle whose length is (a-x) then its centre should be (a-x)/2. am i right sir?

[@ofentsemosima3363]

YOU ARE RIGHT. VERY RIGHT I GEZ!

[@varunagajoashan1054]

East or west u r d best

[@beoptimistic5853]

kzbin.info/www/bejne/joKsk6FobMmCoKc 💐💐

[@manikkumar8171]

when dA =dydx then how it can be solved??

[@jenna943]

You use dL = root( (dx)^2 + (dy)^2 ). Then, choose which integration is needed and solve. dL should look something like dL = root( (dx/dy)^2 + 1 ) dy.

[@DistinCtiveMoody]

U R the best

[@therelaxationpoint]

Thank x from India..

[@prateekamrawanshi505]

Great video

[@MichelvanBiezen]

Thanks!

[@nagalingeswararao1547]

Thank you so much sir

[@auliamuhardiarifin8427]

what if y = ax^2 + bx + c ? we just cant convert x into y, the x is still remain

[@MichelvanBiezen]

You can always convert your vertex position so that the constants b and c go to zero, and you will get the exact same result. That is why this general technique works for all such examples.

[@sibomanaemmanuel6352]

It's not visible

[@MichelvanBiezen]

What is not visible?

[@zero_kelvin_]

the entire 2nd half was for nothing... thanks alot

[@raajithaindurthi5181]

Thank you sir

[@muhdizzlan974]

very nice

[@motosmas860]

Best teacher :D thanks

[@MartinBuyi]

I now learn things I failed to learn from class

[@arturaskarbocius6091]

My kitty finds mass of gravity in mid flight without any calculus knowledge :)))))))))))

[@rabeash711]

Thanks alot

[@زكيالمنصوري-ي5ث]

Thank you

[@ahmedal-ebrashy3691]

Wow, cant get this right no matter what I do, will try again though

[@beoptimistic5853]

kzbin.info/www/bejne/joKsk6FobMmCoKc 💐💐

[@زكيالمنصوري-ي5ث]

Thank you teacher

[@beoptimistic5853]

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[@ayasguitar8718]

Man u saved me from failing

[@MichelvanBiezen]

Glad to hear it. Keep it going.

[@montanodoradogonzalojunior1848]

Buenísimo video

[@garyschiffer4576]

Thanks sir!

[@beoptimistic5853]

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[@VibudaJayathilake]

learning in 2021! (5/1/2021)

[@beoptimistic5853]

kzbin.info/www/bejne/joKsk6FobMmCoKc 💐💐

[@براءمحمد-ق7ت]

Thanks

[@anilkumarsharma8901]

center of gravity of mountain ????like a prism ??? like a pyramid ???

[@fifalovers449]

Thanks from pakistan .

[@MichelvanBiezen]

Welcome to the channel.

[@michaelduke1405]

Too complicated...

[@skbrajraj831]

second part for finding the x bar could be done in much simple way .... you unnecessarily made it complicated

[@MichelvanBiezen]

Yes, but the purpose of the video is to show the various techniques, such that a greater understanding can be reached

[@pi17]

(Very useful for class 12th)⁴ (Thanks)ⁿ; n≥8

[@arjunsatheeshan9761]

30 dislike by commerce students

[@mohammadzaher2737]

يا لعيب

[@brianramz6681]

when he say H but he keeps on writing R lol

[@beoptimistic5853]

kzbin.info/www/bejne/joKsk6FobMmCoKc 💐💐

[@mr.papalavaskia9795]

thank you

[@MichelvanBiezen]

You're welcome