How to Calculate the Center of Gravity of the 2D Objects?

How to Calculate the Center of Gravity of the 2D Objects?

The Center of gravity is a very important phenomenon for calculating the balance of the systems. The center of gravity of the compound systems must be calculated carefully and the placements of other components must be made according to the center of gravity balance. 

In this article, we will show you how to calculate the center of gravities of the 2D and 3D objects and what is the difference between them. 

Gravity Center Calculation for 2D Objects

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2D objects are not real-life stuff. They are used in theoretical applications. 2D objects are also used as an approximation in calculations if the third dimension of the objects is the same. The Center of calculation of the 2D objects is simpler than the 3D objects, and because of this, it is generally used to make the calculations simple. 

Take a look at the simple example below about the center of gravity calculation for 2D objects. 

There are 3 objects named ‘A’, ‘B’ and ‘C’. And because these objects are 2D, only X and Y coordinates are in the stage. 

Object A; (x, y) = (3, 5), Mass = 10kg. 

Object B; (x, y) = (-8, 4), Mass = 5kg.

Object B; (x, y) = (2, 4), Mass = 3kg.

To find the center of gravity of these three objects combined, first, we need to find the center of gravities in X and Y coordinates separately. 

To do it, we need to multiply the X coordinates with the masses and sum up all the results. Then divide this result by the total mass. 

Gx = (Xa*Ma + Xb*Mb + Xc*Mc)/(Ma+Mb+Mc); 

= (3*10 + (-8)*10 + 2*3)/18; 

Gx = -2.44. 

Lets do the same calculation for the Y coordinates; 

Gy = (Ya*Ma + Yb*Mb + Yc*Mc)/(Ma+Mb+Mc); 

= (5*10 + 4*10 + 4*3)/18; 

Gy = 5.6. 

As a result, the total center of gravity of the 3 of 2D objects combined is; 

G = (Gx, Gy) = (-2.44, 5.6). 

Center of Gravity Calculator for 2D Objects

You can use the center of gravity calculator that is prepared by us to calculate the center of gravities of 2D objects. 

The use of the center of gravity calculator is very simple. You just need to select which dimension you want to make your calculation 2D or 3D. Select 2D and enter the number of masses that you want to calculate the center of gravity. Then it will ask you all the required coordinate places of these objects and masses. Click on the ‘Calculate!’ button to calculate the center of gravity of the 2D objects. You can click on the ‘Reset’ button and re-enter to values to make another center of gravity calculation. 

Conclusion

Calculation of the center of gravities of 2D objects is very simple like above. 

Do not forget to leave your comments and questions below about the calculation of gravity centers of 2D objects.

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