Centroid is the term that applies to a geometrically balanced figure or an object. It is the center of that figure or object. The methods to find the center of a symmetrical entity differs, but it exists, and there is no confusion about that.
For example, a triangle has the centroid which is the meeting point of three medians. In contrast to the centroid, the center of gravity is a broader term that encompasses symmetrical and asymmetrical objects and figures. It is interesting to note that the center of gravity and the centroid are the same for a symmetrical object as well as volumetric figures and shapes. For asymmetrical objects, we need to do a weightdistance analysis and find the average by dividing it by the total weight to find the distance of COG. The figure below gives an idea of how we can perceive both these concepts
Fig:1 Centre of gravity of irregular stones and the Centroid of Trapezium
The Centre of gravity and centroid tend to be the same for two-dimensional figures and volumetric figures and is important to know because of the stability and balance it provides. In the above figure, the center of gravity of irregular stones will shift to the left due to the tilt presented while arranging them one by one and due to the irregular shapes of the stones. In the case of trapezium, the formula is given in the figure once you have a, b and h. This article gives clarity to the concept of the center of gravity and centroid. Both of them are very closely related terms in terms of centering or stability of a volume or mass object but differ under certain circumstances.
The Centre of gravity is the imaginary point in an object through which the earth’s gravitational force acts on the material mass of an object to create its weight. It is at that point the entire weight is focused to provide the required stability for that object.
The equation Weight = Mass $\mathrm{\times}$ Gravitational Force;W = mg is worth mentioning here. The center of gravity is the distance from a reference point on the object. So the unit by which it is measured is in meters.
The importance of the center of gravity is well understood if you take the example of the stability of automobiles. Cars, trucks, and vehicles have a very strict design phase where the manufacturers test the COG of the vehicle to be as low as possible when satisfying all other requirements. The lower the COG is; the better stability is for the vehicle on road.
Referring to the figure below, the rod is having two weights at two ends - W1(5kg) acting at point A and W2(2kg) acting at point B. With this weight distribution, the center of gravity is acting at point G.
Fig:2 Find the center of gravity
With x1 and x2 distances marked in the figure, the equation for distance x (COG) will be
$$\mathrm{x=\frac{(x_{1}W_{1}+x_{2}W_{2})}{(W_{1}+W_{2})}}$$
The Centre of gravity is an imaginary point in the object where the weight of the object acts downward due to the effect of the earth’s gravitational force. The Centre of mass is the point in the object matter, where external force acting in the object would make its effect of moving in the direction intended by the external force.
No other factors other than the intended direction are connected with the point identified as the center of mass. In many scenarios, both of these would converge to the same point. But both are not the same always. COG acts downward due to gravity, while in contrast, COM acts in the intended direction of external force.
Q1. Find the centroid of a straight line of length 10m?
Ans. Centroid of the line is
$$\mathrm{\frac{L}{2}=\frac{10}{2}=5\:meter}$$
Q2. Find the centroid of a circle of area A?
Ans. Centroid of a circle is radius r.
$$\mathrm{A=\pi r^{2};So\:r=\sqrt{\frac{A}{\pi }}}$$
Q3. Find the centroid of a rectangle of length a and breadth b?
Ans. X coordinates of the centroid of the rectangle are $\mathrm{a/2}$ and Y coordinate is $\mathrm{b/2}$
Since the centroid or COG of geometrical figures is based on geometrical principles, refer to the formula for all possible figures with a good reference.
Centroid is the term considered where geometrical figures without mass are considered like circles, triangles, squares, trapezoids, etc. When objects with mass and weight are considered, the center of gravity is the term used.
| S.NO | Characteristic | Centre Of Gravity | Centroid |
|---|---|---|---|
| 1 | Direction of force | Vertically downwards | In the direction of external force |
| 2 | Main Criteria | Weight | Geometric Centre |
| 3 | Denoted By | Point G | Point C |
| 4 | Calculation / Measurement | By physical properties | By geometrical methods |
| 5 | Density | Variation in density within object allowed | Uniform density of the geometrical pattern or figure |
| 6 | Demonstration | Can be demonstrated with a physical matter of symmetrical or asymmetrical mass/density distribution | Can be demonstrated using geometrical concepts and validation of same. |
Two interesting concepts were detailed in this article. The common idea in both is symmetry and balancing tone. Each of these topics were explored in terms of definition, core concept, equations, relation with the center of mass, practice problems, and last but not least, the differences between two - centroid and center of gravity. It is interesting to note that both these become the same in most instances like volumetric shapes and figures; they are the same and can be switched to each other. For asymmetric materials with mass, both are distinct and different. For symmetric materials with mass, again, they can be switched to each other, because they converge to the same point in the body matter.
Q1. How can you find the centroid of a sphere?
Ans. If you consider a sphere in an x-y-z coordinate plane, and if its center is in origin, then the centroid of that sphere is the origin itself. If you are taking from the surface of the sphere, it is r (radius) distance from any point on the surface.
Q2. What is the unit of the center of gravity?
Ans. It is distance and hence unit is in meters.
Q3. What is the center of gravity in Operations?
Ans. Centre of gravity is the lowest operating cost center among multiple centers for a specific operation.
Q4. Will EV vehicles with batteries attached to chassis provide better stability to cars?
Ans. Yes, it is a welcome side-effect. The batteries by design are best to be accommodated on the floor for protection and space conservation. It is a bonus that this reduces the center of gravity of the vehicle and thus reduces rollover of vehicles and accidents.
Q5. What is a moment of mass?
Ans. The moment of a mass is the product of mass and distance from a point.
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