The Center of gravity is a very important part of physics and engineering. To balance the separate masses on physical and engineering systems, you need to calculate the center of gravity. Separate masses and parts can affect the whole machinery’s balance.
In this article, we will explain how to calculate the center of gravities of 3D objects by hand and with a calculator.
How to Calculate the Center of Gravity of the 3D Objects?
Instead of 2D objects, 3D objects are used in most of the machinery. 2D objects are generally used in the simplification of the calculations for which the 3rd dimensions of parts are the same. If they are not the same, the 3D center of gravity calculations must be implemented.
Take a look at the very basic example below. Here, we have three objects named ‘A’, ‘B’, and ‘C’. The information about the masses and positions in coordinate systems of these objects is like this;
Object A: (x, y, z) = (2, 5, 7); Mass 7kg.
Object B: (x, y, z) = (-3, 5, -6); Mass 3kg.
Object C: (x, y, z) = (0, -8, 2); Mass 10kg.
Think about the machinery that is constituted by these objects or parts. And we would like to calculate the center of gravity of this machinery. First of all, we need to calculate the center of gravities in each coordinate. To do it, we need to multiply the masses of each object with the X coordinate of each object. Then divide this calculation by the total mass of the objects to find the center of gravity in X coordinates.
Gx = (Ma*Xa + Mb*Xb + Mx*Xc)/(Ma+Mb+Mc);
Gx = (7*2 + 3*(-3) + 10*0)/(7+3+10);
Gx = 0.25.
The total center of gravity of the system is 0.25 in X coordinates.
Let’s do the same calculation for Y and Z coordinates.
Gy = (Ma*Ya + Mb*Yb + Mx*Yc)/(Ma+Mb+Mc);
Gy = (7*5 + 3*5 + 10*(-8))/(7+3+10);
Gy = -1,5.
So the total center of gravity of the machinery in the Y coordinate is -1.5.
For Z coordinates;
Gz = (Ma*Za + Mb*Zb + Mx*Zc)/(Ma+Mb+Mc);
Gz = (7*7 + 3*(-6) + 10*2)/(7+3+10);
Gz = 2.55.
The total center of gravity of the machinery in the Z coordinate is 2.55.
The total center of gravity of the three objects in 3D space is;
G = (Gx, Gy, Gz) = (0.25, -1.5, 2.55).
Calculation with Center of Gravity Calculator
We provided a center of gravity calculator to use in these calculations. The calculation above can be made in the center of gravity calculator. First of all, you just need to select the ‘3D’ and enter the number of masses that you want to make the center of gravity calculation. Enter the required values that the calculator asks. Click on the ‘Calculate!’ button after entering each separate value. Then finally you will see the result. If you want to make another calculation, just click on the ‘ Reset’ button to do it.
As you see above, the calculation of gravity centers of 3D objects is very simple.
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