What is Centroids: Definition and 24 Discussions

In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the figure. Informally, it is the point at which a cutout of the shape (with uniformly distributed mass) could be perfectly balanced on the tip of a pin. The same definition extends to any object in n-dimensional space.While in geometry, the word barycenter is a synonym for centroid, in astrophysics and astronomy, the barycenter is the center of mass of two or more bodies that orbit one another. In physics, the center of mass is the arithmetic mean of all points weighted by the local density or specific weight. If a physical object has uniform density, then its center of mass is the same as the centroid of its shape.
In geography, the centroid of a radial projection of a region of the Earth's surface to sea level is the region's geographical center.

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  1. Tapias5000

    Solving the Weight Puzzle: Explaining Why and How

    My solution is However can someone explain in detail why will be equal to the weight? and why does it have to be multiplied by 6?
  2. Tapias5000

    How can I locate the coordinates of the centroid of a cone in Z?

    This is the picture of the problem. My solution is: I'm not sure if the limit is 0 to 2 or 0 to 4...
  3. circuit232

    I Centroid Problem Solutions: Integrate or Otherwise?

    Is there any other way to solve a centroid problem other than integration?
  4. P

    How is the mass of the composite shape calculated using centroids and statics?

    Hi can anyone explain how in this solution they were getting for the rectangle 175x210. And how they split the triangles Thank you
  5. D

    Centre of Gravity and Centroids

    Homework Statement http://puu.sh/lJgzB/5b877de108.jpg http://puu.sh/lJgAR/c28393f051.jpg Can someone please explain these two slides to me? Especially the first one, It seems to be summing the Moments in y and Moments in x. The sum of the moments in y is xW. I understand that but then it...
  6. B

    Find Centroids: Determine Ix'y' for Area - a=120mm, b=290mm, d=30mm, h=390mm

    Homework Statement Determine the product of inertia of this area with respect to the centroidal x′ and y′ axes. Locate the centroid x bar of the beam's cross-sectional area. Set a = 120mm , b = 290mm , d = 30mm , h = 390mm . Homework Equations ? The Attempt at a Solution So I can't find...
  7. Chris L T521

    MHB Jamie's question from Yahoo Answers regarding centroids

    Here is the question. Here is a link to the question: Centroid of x+y=2 x=y^2? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  8. J

    Statics, centroids of lines, areas and volumes

    Hi to everybody. I´m reading a book about statics and I cannot understand this chapter. I have been calculating moments of forces in hundreds of problems, when I found a force acting on a body I needed to fix a coordinate system, then calculating the moment arms of that force around a point...
  9. T

    Finding the combined centroid of two regions given the centroids of both regions

    Homework Statement The Attempt at a Solution I tried to do this problem by taking the average of the y-bar centroid values but that gave me the wrong answer. I am only interesting in knowing why this method is incorrect. Thanks!
  10. P

    Reference frame to calculate centroids

    Hi. I was recently calculating some centroids and I was wondering if the point were I choose my origin affects the centroid position. I.e., if I choose my origin at a massive particle, will the centroid be the same as with any other reference frame? Thansk :)
  11. T

    Applications of Double Integrals: Centroids and Symmetry

    Homework Statement A lamina occupies the region inside the circle x2+y2=2y but outside the circle x2+y2=1. Find the center of mass if the density at any point is inversely proportional to its distance from the origin. Here is the solution...
  12. P

    Intuition behind Centroids / Center of Mass

    Hi all, I've been digging around in Google as well as searching under physics forum for a while now but I still can't find the answer to my question. If there is already an answer then I'm sorry for wasting the server bandwith and database harddrive usage I learned the formulation for...
  13. M

    Centroid Question: Proving AM=2AG using Law of Centroids and (A,2),(B,1),(C,1)

    Homework Statement (A,2),(B,1),(C,1) and M is the center of [BC] and N is the centroid of: (A,2) and (B,1) Homework Equations show that AM=2AGThe Attempt at a Solution I used the law and i got 4AG=2AM+0.5MB +0.5MC But what did i do wrong?
  14. B

    Centroids of a structural Shape

    I have a problem trying to find the centroid. I have a plate that is 8in wide and .5 in thick. Then 2- C beams (C8x11.5) placed at each end of the 8in beam with the tips facing each other. They do not go beyond the 8 inches. So it's like a U as an example with the tips facing each other. I...
  15. R

    Centroids of two and three dimensional figures

    In my Questions I usually have to calculate the Centroid of a curve whose equation is given! I don't know the formula which are used it that, and I have searched on google too and couldn't find anything useful. Can someone provide me with formulas for how to calculate centroid of 2 and 3...
  16. M

    Centroids please need a bit of help

    I'm not sure wether the top shape triangle the x-axis should be minus or plus. i've got all the areas including x1 x2 x3 x4 and y1 y2 y3 y4 since I've splited the whole shape into 4 shapes (2 triangle and 1 square and 1 rectangle).would appreaciate if anyone can help me out with it...
  17. S

    Centroids Simplifying by symmetry

    If you have a 3d shape how do you simplify the problem using symmetry. eg with a sphere is symmetric along any axis therefore the centroid must be in the middle of it eg2 A cone sitting on the xy plane, where the pointy bit is points up the z axis. -nb it is sitting on point (0,0,0) where the...
  18. T

    Finding volumes of revolution using centroids

    In my Cal II, we're discussing finding volumes of revolution using centroids, which we find using moments of x or y. Can someone explain to me what a moment is?
  19. T

    Video about how to find centroids?

    dose anyone know a website that has a video about how to find centroids?
  20. B

    Statics Problem (centroids)

    Hey, I'm wondering if anyone could possibly explain to me how to find the tension forces present in a problem consisting of: A composite shaped plate, being hung by two wires. First the problem asks to determine the center of gravity/centroid of the shape, then to determine the Tension forces...
  21. Z

    Centroids of various triangles.

    I've been having some confusions regarding the centroid coordinates of triangles. I've been taught that the centroid of a triangle lies at 1/3rd of the perpendicular distance from any selected base to the corresponding top point of the triangle. I tried to use this shortcut to find the...
  22. P

    Finding centroids when integrating with respect to y

    Homework Statement no specific problemsHomework Equations x center of mass = moment about y/total area y center of mass = moment about x/total area The Attempt at a Solution ok, so I am in AP calculus, and since the AP testing has ended, we've done some random topics, such as centroids of...
  23. P

    Finding Centroids: Self-Tutoring & Simple Examples

    I'm doing a little self tutoring here, but I'm having trouble finding centroids for geometric shapes. I have a book that gives the formula for x and y coordinates (something like x = int(x dA)/int(dA) and similar for y). I still don't understand it though. Can someone explain it in more detail...
  24. P

    Centroids and Center of Gravity

    The homoegeneous wire ABCD is bent as shown and is supported by a pin at B. Knowing that l=8, determine the angle theta for which portion BC of the wire is horizontal. Below is the free body diagram with the forces exerted by the pin indicated by the two arrows on the wire. How do I approach...