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Questions tagged [centroid]

"The centroid or geometric center of a plane or solid figure is the arithmetic mean ("average") position of all the points in the shape. "

This tag is for questions about the centroid of a geometrical shape, its properties and computation.

The centroid or geometric center of a plane or solid figure is the arithmetic mean ("average") position of all the points in the shape. The notion generalizes immediately to n-dimensional figures.

If a solid body has uniform mass density, the centroid agrees with its center of mass.

This tag is for questions about the centroid of a geometrical shape, properties and computation.

Use the tag if the question relates to the geometrical properties of the centroid.

Use the or tag if the question relates to finding the centroid of an object by integration.

283 questions
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Centroid of connected 3D shapes

This might be a dumb question, but I tried to search for answers online and couldn't find any. I couldn't find too much information about centre of mass of irregular 3D objects in general. So, I have three 3D shapes which are connected to each…
Ana
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Centroid of a plane figure of a plane figure.

A plane figure is enclosed by the parabola $y^2 =4x$ and the line $y=2x$. Determine the position of the centroid of the figure. Here is what I tried : Plotted the graph. $y=4ax, y=2x \\ 4x(x-1)=0 \quad x=1, x=0\\$ $\bar{x}=\frac{\int xy \mathrm{dx}…
Orestes Dante
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When filing up any shaped vessel with a liquid, is the lowest total centre of mass when the liquid level reaches the total centre of mass

When you have an empty cylindrical cup the centre of mass is about halfway up, the same is true with a full cup, but partly full and the combined centre of mass of cup and liquid is below hafway. I found out that for a prism being filled up…
user148667
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Coordinates of centroid of a triangle

If $A(x_1,y_1) , B(x_2,y_2) , C(x_3,y_3)$ be the vertices of a triangle then prove that coordinates of centroid are given by $(\frac{(x_1 + x_2 + x_3)}3 , \frac{(y_1 + y_2 + y_3)}3)$
Slow learner
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Find the exact coordinates of the centroid for the region bounded by the curves $y=\frac 1x$, $y=x$, $y=0$ and $x=2$

Im not sure how to set up these integrals. I tried using $y=x$ as the upper curve and subtract $y=\frac 1x$ in my integrals but I still am not getting the correct answer. If anyone knows how to do this and could help me out it would be greatly…
Emiel Winkelmolen
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Using the Pappus and Gulin Theorem. To derive the formula V = 2pi(xbar)A

(a). Write down a formula for the volume V of the solid obtained by revolving the region R about the y-axis. I think: $\displaystyle\int_{x=a}^{x=b}[f(x) - g(x)]*(2\pi(x))dx$ (b). Write down the formula for the moment M_y of R about the y-axis. I…
Foo Fighter
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Center of mass - Semicircular arc centroid

I'm doing exercise 5/5 from STATICS Meriam 6th to find center of mass Y that's the resolution: 1º - I couldn't understand well dA. Arc lenght (choosen centroid) is ** $ \pi * dr $ ** but why times R (R $ \pi $ dR)? 2º - From table of commons…
Goldman7911
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How do I find the moments and center of mass of a Lamina with given density?

I am trying to solve for the center of mass of the shape given below. I started by finding the area of the shape, which is $A = Atriangle + Acircle/4$ $ = 1/2 + pi/4$ $=(2+pi)/4$ then I used the formula $(1/A) \int [(sqrt(x^2-1))^2 - (x-1)^2] dx$…
Niko H
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Finding centroid of an area

why should the integral be multiplied by 1/2 for finding the y bar? I dont understand that. Thanks!
Ann
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