How to find the centroid of the area under a parabola

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This engineering statics tutorial goes over how to find the centroid of the area under a parabola. It requires a simple integration.
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Thanks for watching, I hope it helps!

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1 окт 2024

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Комментарии : 32

@johnsandas2335 5 лет назад

you would find y(bar) by using the same dA; however, your you would have to divide the y(tilda) by 2 because you differential's centroid is half of the y. In other words the height of your differential is y, so the centroid(y aspect) of the rectangle is y/2. This gives y(bar)== integral((y/2)(dA)). Since the dA is the same, the bounds also stay the same: 0 to 4

@sundod 9 месяцев назад

you save our lives 🐐

@DaveMatthewYoutube 9 месяцев назад

@@sundod you have some pretty recent reply

@ahmeddeghady4510 6 лет назад

Thank You! Getting Y point is not clear enough but X's part was well explained.

@harsevsingh6596 4 года назад

2 months into a Mech Eng degree.....your channel has just become my best friend

@Engineer4Free 4 года назад

That’s awesome!! Tell some other friends too please 🙂🙂

@notaturtle561 7 лет назад

You say to find Y bar one must do it all again (in terms of y?). Is it just function of X bar? (I just graduated hs, so hopefully this isn't a silly question)

@Engineer4Free 7 лет назад

Sorry maybe I wasn't clear enough about that! Any point y on the curve of the parabola is a function of x and can be found with y=x^2 .The centroid does not lay on the curve, and rightfully so because it is the "center of area" for the shape. I only found the x component of the centroid, which is commonly named x bar. I made no attempt to find the y component of the centroid, which is called y bar. Don't get y bar confused with the y component of the curve at x = x bar! You solve for y bar with a similar equation, only integrating along the y axis. Here is a solution for x bar and y bar that covers any type of variation of this problem: www.mathalino.com/reviewer/engineering-mechanics/708-centroid-and-area-spandrel-integration If you expand the solution, you'll see that the last part is where they find y bar. PS congrats on graduating!! Why are you still watching engineering videos on RU-vid? :p

@notaturtle561 7 лет назад

Now I realize my question was obvious. Thank you! (I'm going to college and I want to be ready!)

@Engineer4Free 7 лет назад

Oh you graduated high school! I thought you meant you just graduated college for some reason haha. Good job getting an early start, it will pay off!! I'm always adding more courses, so stick around :)

@ashishupadhaya8532 3 года назад

@@Engineer4Free why is yc taken y/2 while integrating

@itumelengmaleka5904 3 года назад

Thank you so much I feel like my journey to becoming an engineer is clearer

@Engineer4Free 3 года назад

Glad to hear that! Many more vids on the channel :]

@mujibrahman8623 4 года назад

Y r u calculating decimal values instead of cancelling the squares and cubes.

@Engineer4Free 4 года назад

That would have worked as well

@mujibrahman8623 4 года назад

@@Engineer4Free but u need calculator for that

@antoniopensanti4534 Год назад

solving for the x direction makes a ton of sense to me. The y I have no idea. Our teacher wants us to solve the integrals and I dont even know where to begin for the y

@RafaelRodriguez-km9nx 4 года назад

"Yc" was not done.!!!

@Engineer4Free 4 года назад

Yeah sorry that was an oversight on my behalf when I made the video. I only found the x component because in almost every statics distributed load problem, you only need the x component. This video is a set up to some more statics videos on distributed loads.

@mpmccormick1 5 лет назад

would have like to see y-bar, too

@Engineer4Free 5 лет назад

Yeah my bad. I only solved for xbar because the next videos in the series get into distributed loads on beams where you only need to know xbar and ybar is irrelevant.

@bickybong8992 5 лет назад

Love your vids! Wanna know if there is one about the second moment of area tho as I can't seem to find it

@Engineer4Free 5 лет назад

Yeah check videos 29-34 here: engineer4free.com/mechanics-of-materials some of them deal with that second moment as the +Ad^2 term. I think that's what you're asking for.

@Endermage1244 5 лет назад

yeah we need the y spot as well

@emirerdem5769 3 года назад

same here :)

@simpleintertainmetvideos3227 5 лет назад

Thanks sir

@Engineer4Free 5 лет назад

You're welcome!!

@gustavosh.5147 6 лет назад

Great videos, but i was kinda hoping I'd find something about inertia in depth like other videos.

@Engineer4Free 6 лет назад

Hey thanks for watching. I recommend checking out videos #25 - 34 here: engineer4free.com/mechanics-of-materials for some explanation and examples for moment of inertia. Videos 22 - 24 there might provide some helpful context on the matter too. Cheers

@gustavosh.5147 6 лет назад

Thanks for fast reply. Great videos. I'll make sure to watch mechanics of materials looking for moment of inertia. 👍