Centroid,centre of mass and centre of gravity

In summary, centres of mass, gravity, and centroid refer to different points on an object. Centres of mass and gravity are calculated based on a uniform gravitational field, while the centroid is calculated based on a non-uniform gravitational field. Geostationary altitude is the altitude where the center of mass and center of gravity are the same.
  • #1
monty37
225
1
may i know what is the difference between centroid,centre of gravity and centre of mass
of a body?is it necessary that all the points coincide?
 
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  • #2
Those all mean the same thing.
 
  • #3
monty37 said:
may i know what is the difference between centroid,centre of gravity and centre of mass
of a body?is it necessary that all the points coincide?

Take a triangle for example.

The centroid is the mean position of elements of area.
The centre of mass is the mean position of elements of mass.
In a uniform gravitaional field, the force of gravity on the triangle
can be taken as acting through the centre of mass.

But if the mass per unit area of the triangle varied, the centre of mass
would not (usually) coincide with the centroid.

Note also that the assumption that the Earth's gravity is the same
as if its mass were all located at the centre is only true because of
its spherical symmetry.
 
Last edited:
  • #4
"centroid" is a purely mathematical, geometric concept- the geometric center of a body. It can be calculated as the center of mass of an object with constant density. "Center of mass" and "center of gravity" are the same- although the concepts are slightly different: the concept "center of gravity" strictly speaking requires, as davieddy said, a uniform gravitational field while "center of mass" does not. But they are exactly the same point on an object.
 
  • #5
An alternative definition of the center of gravity of an object is the point at which the gravitational force on a point mass located at the point in question is equal to the total gravitational force acting on the object. The concept of center of gravity in a uniform gravitational field doesn't make sense with this alternate definition. It only makes sense in a non-uniform gravitational field.

With a gravity field that falls off linearly with distance, center of mass and center of gravity are the same. However, with a gravity field that falls off with the inverse square of distance, center of gravity and center of mass are not the same. For a small object, say something the size of the space station, the difference between center of mass and center of gravity is very small because the first order linear approximation is very, very good.

For a large object, say something the size of a space elevator, center of mass and center of gravity are very different. Lay literature on a space elevator often claim the center of mass needs to be at geostationary altitude. This is incorrect. It is the center of gravity that needs to be at geostationary altitude. The center of mass needs to be well above geostationary altitude.
 
  • #6
iam clear about the three,but can you please explain the "geostationary altitude "?
for the Earth as such ,a sphere,all the three points coincide ,right?
 

1. What is the difference between centroid, centre of mass, and centre of gravity?

The centroid is the geometric center of a shape, while the center of mass is the point at which the mass of an object is evenly distributed. The center of gravity is the point at which the force of gravity acts on an object. For most objects on Earth, the center of mass and center of gravity are the same. However, for objects in space or on non-uniform gravitational fields, the center of mass and center of gravity may be different.

2. How is the centroid calculated?

The centroid of a shape can be calculated by finding the average of the x and y coordinates of all the points in the shape. For irregular shapes, the centroid can also be calculated by dividing the shape into smaller, simpler shapes and finding the centroids of those shapes.

3. How does the centroid affect the stability of an object?

The centroid is an important factor in the stability of an object. An object is most stable when its center of mass is directly above its base or support. If the center of mass is outside of the base, the object may topple over. Therefore, the lower the centroid, the more stable the object.

4. Can the centroid change?

The centroid of a shape will remain the same regardless of the orientation or position of the object. However, if the shape of the object changes, the centroid will also change accordingly.

5. How are centroid, centre of mass, and centre of gravity used in real-world applications?

These concepts are used in various fields such as engineering, physics, and architecture to design structures that are stable and balanced. They are also important in understanding the motion of objects and predicting their behavior in different environments.

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