# Center of Gravity

We must understand that a body is a distribution form continuous of mass , and each of its parts involving the force of gravity . The center of gravity or centroid as it is also known, is the position where the net force of gravity acts , it is a point that is located in the place where the total weight of the body is concentrated . For an object that is symmetrical and homogeneous in shape , the center of gravity is located at the geometric center , otherwise in an irregular object.

Formula

Mg (r cg .) = ∫ v g (r) p (r) dV

cg x Mg (r cg ) = ∫ v  rxg (r) p (r) dV

## What is the center of gravity?

The center of gravity is the point of application that is obtained from the resultant of the forces of gravity that act on the different material parts that a body has, producing a null resultant .

• Definition
• What is the center of gravity for?
• Properties
• Calculate the center of gravity
• Experiments
• Importance
• Center of gravity of a triangle
• Other examples

## Definition

The center of gravity is the point of application of the resultant of all the forces of gravity that intervene on the different material masses that a body has , in such a way that the moment related to any point of this resultant applied to the center of gravity will be the same as that produced by the weights of all the material masses that make up the body. In other words, we can say that the center of gravity is the point at which the forces exerted by gravity on the material points that make up the body cause a momentnull resultant .

## What is the center of gravity for?

The center of gravity is the place where the moments of inertia and mass are concentrated , it serves to be able to make calculations about the volume of bodies, it is the equilibrium point that objects have, it helps the human being to maintain an adequate position and to be able to walk and provides stability to motor vehicles preventing them from tipping over.

## Properties

There are three properties that the center of gravity has, these are:

• The resultant of the gravitational forces acting on the particles of a body can be replaced by a single force, the body’s own weight , which is applied at the body’s center of gravity.
• An object on a flat base will be in stable equilibrium if the vertical passing through the center of gravity cuts the base of support .
• When the body moves slightly away from the equilibrium position, a restorative moment will arise, recovering the initial equilibrium position . If you move away, the center of gravity may move out of the base of support and then there will be no restorative moment causing the body to move out of position.

## Calculate the center of gravity

The center of gravity is calculated following the formula:

Mg (r cg .) = ∫ v g (r) p (r) dV

cg x Mg (r cg ) = ∫ v  rxg (r) p (r) dV

Where

• M refers to the total mass of the body.
• G is the gravitational field
• D is the distance

## Experiments

An experiment that we can carry out to check the center of gravity of an object is the following:

Materials:

• Rule
• Candle
• Needle
• Two crystal goblets
• Lighter
• Gripper

Procedure : the hot needle must be pierced exactly in the center of the candle . Then, it is placed balancing between the two cups.

Explanation : when the candle is lit at one end, an amount of mass is lost causing the candle to lose the center of balance and fall, but when we quickly light the opposite end of the candle, the mass will be lost on both sides causing the center to fall. mass change position , so the candle will present very large oscillations .

## Importance

Its importance lies in the fact that knowing the center of gravity we have the possibility of being able to solve different problems related to mechanics , electromagnetism and other branches that are related to physics . Through it, it is possible to study the motion that a rigid body presents and to know the center of mass of the bodies. As for the human being, the center of gravity is of utmost importance because it represents the way in which the body manages to maintain its balance .

## Center of gravity of a triangle

The center of gravity having a triangle is also known of barycenter or centroid and the term refers to the point where the three concur medium having the triangle. These medians are the segments that join one of the vertices of the triangle with the center of the side that is opposite. The distance between the center of gravity and the vertex is twice the distance between the center of gravity and the opposite side .

## Other examples

• Center of gravity of the human body
• Center of gravity in aviation
• Center of gravity in motorsports