How to Find the Centroid of a 3D Object EXAMPLE PROBLEM // Center of Mass of Composite Bodies

In this video I go through an example problem on how to find the center of gravity of a 3D composite body with varying density. Check out the steps below for more details.
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Steps to finding the center of mass of a composite body:
1) Establish a coordinate system for the object
2) Break the object up into simpler shapes (composite parts) that you can more easily find the centroid of
3) Find and list the coordinates of the centroid of each composite part
4) Calculate and list the area (or volume for 3D objects) of each composite part
5) Plug the coordinates of the centroid and the areas into the following equations
x ̅=(Σ x ̃*A)/(Σ A) y ̅=(Σ y ̃*A)/(Σ A) z ̅=(Σ z ̃*A)/(Σ A)
where x ̃,y ̃,and z ̃ are the x, y, and z coordinates respectively of the center of mass of a composite part and A is the area of a composite part. If you are dealing with a 3D object then replace A with the volume of each component part. Each coordinate is multiplied by the area or volume of that same composite shape. x ̅,y ̅,and z ̅ are the x, y, and z coordinates respectively of the entire area or object.
Notes:
- In order for the above process to work to find the centroid of an object, it must be of constant density. If the entire object is not of constant density then you break it up into components that are of constant density and in the equations you replace volume with mass or weight. Remember that mass is the volume multiplied by density.
- If the object is symmetrical about an axis, then centroid will lie on that axis of symmetry and you will not need to calculate the one of the coordinates of the centroid. For example, if a 2D object is symmetrical about the y axis then you will not need to calculate the x coordinate of the centroid x ̅.

[@floppyfrijole]

Thank you so much for this clear and precise explanation!

[@studentengineering]

You’re welcome!

[@RealLifeTop10s]

Thank you so much for this video!
It was very helpful!
You explained it very clearly!

[@studentengineering]

You’re welcome!

[@juhenfw_]

Thanks for the explanation sir, very helpful for me

[@studentengineering]

You’re welcome! I’m glad it was helpful!

[@godwincornelius201]

Thanks a lot sir. You are really good at explaining things

[@studentengineering]

Thanks I appreciate that!

[@tahmidurrahman6091]

thanks man ur video is so nice. just clear my concept of this topic very well thank u so much

[@studentengineering]

You’re welcome! I’m glad you liked it

[@tayeebahtamanna3344]

Thanks a lot...your explanation helped me a lot

[@studentengineering]

I’m glad!

[@CuteAlsoFunnyAnimals]

Thank you so much this helped me a ton

[@studentengineering]

You’re welcome! I’m glad it helped

[@aleksandroleinikov8453]

Very useful video!

[@studentengineering]

I’m glad you thought so

[@Skuliosis]

ty for the vids

[@studentengineering]

You’re welcome!

[@vinodengineer5694]

Thank you sir😊🙏

[@studentengineering]

You’re welcome!

[@mohammadshabih5293]

thank you

[@studentengineering]

You’re welcome!

[@gnidnoeled786]

Would you please show us how to find the centroid of the irregular solid according to the following descriptions.
Rectangle:
Along X direction = 3.8
Along Y direction = 2.5
At the corners of that rectangle along Z direction:
corner A = -95
corner B = -150
corner C = -290
corner D = -230.
Corner A is at the bottom left of the rectangle. Corners B to D is counter clockwise from corner A.
Thanks in advance.

[@studentengineering]

Using the instructions in this video you can find the centroid of that irregular solid. I’m not going to make a another video specifically for this problem

[@mustafaata942]

💜Thanks

[@studentengineering]

You’re welcome!

[@nurulzawani8168]

Sir, may I know how to get the values 2.7, 5.7, 7.8 Mg/mm3?

[@studentengineering]

Those were just given in the problem statement.