The Centre Of Gravity

When Earth produces a force of attraction on a body or surface, it is termed Earth’s gravitational pull. When there’s a force on a body, there’s acceleration. Hence anything that has a gravitational pull will have acceleration due to gravity at the centre of earth. As we move towards the centre of the earth, the value of mass keeps on decreasing. Hence the value of acceleration caused by gravity is measured as zero. 

Formula For Calculating Acceleration Due To Gravity At The Centre Of The Earth: 

g’= g [1- d/R] 

Where g’ is the acceleration due to gravity at depth 

g is the acceleration caused by gravity measured at the earth’s surface. 

And R is the Earth’s radius 

At the centre of the earth r=R 

When we put that in the equation

We get: 

gr= g [1- R/R] = 0 

Define The Term Centre Of Gravity: 

A centre of gravity can also be calculated as the center of mass, from where the weight of a body or an object is measured. 

Calculations made by the centre of gravity are used to design buildings and projects where moving objects and bodies are involved. 

The term centre of gravity and centre of mass is often used interchangeably. They’re not the same,however. The centre of mass of the moon is its geometric centre, whereas the center of gravity of the moon is towards the earth because of its gravitational pull. 

Objects or bodies that are symmetrically shaped have the same centre of mass and centre of gravity. Objects that are asymmetrical or that are made from a variety of materials may have a different centre of mass than their centre of gravity. Objects that are hollow or are irregularly shaped may have their centre of gravity or centre of mass outside of its physical presence. An example could be a tennis ball. 

Measurement Of Centre Of Gravity For regular Shaped Objects: 

When we balance an object through an edge or a string, the starting point of that balance is the centre of gravity for that object. For example, when balancing a pencil on the tip of your finger, the finger is where the centre of gravity for the pencil lies.

Measurement of Centre Of Gravity For Irregular Shaped Objects: 

Hang any object from a point, and also hang a string from that same point. Draw a line along with the object and the weighted string. Then draw another line on the object starting from another point. The point at which these two lines would intersect would be the point of the centre of gravity for the object. 

Importance Of Centre Of Gravity: 

The concept of centre of gravity is important for stabilization. It’s one of the reasons that the top branches of a tree are kept trimmed. Objects with a wider base and lower centre of gravity have maximum stabilization. If the top of an object is heavy or too tall, it is more likely to fall when hit by a force. The automotive industry makes use of the centre of gravity concept in the production of race cars so that they are stabilized in a high acceleration environment. 

Measurement Of Centre Of Gravity Where Mass Is Not Uniformly Distributed: 

By using calculus: 

Symbols s and dw would be used to denote integrated weight. 

Centre of gravity- cg * w = s × dw 

Weight = mass × gravity 

Mass = density × volume 

By combining these two equations we get, 

Weight = gravity × density × volume 

dw = gravity × density × dV 

dw = g* rho (x,y,z) * dx dy dz 

Human Centre Of Gravity:

The human centre of gravity is related to a person’s posture. The centre of gravity is found where the maximum mass of a body is located. In the human body, the centre of gravity is a hypothetical point where there is maximum gravitational pull. According to anatomy, this hypothetical point of centre of gravity lies near the front of the second sacral vertebra. This point of centre of gravity is not fixed however, it keeps on changing whenever there’s movement in our body. It also depends on external factors, such as if we’re carrying some extra weight on our body in case of a suitcase or backpack.

Conclusion: 

The weight of an object is maximum at the point of the centre of gravity. The force of acceleration due to gravity at the centre of earth passes through this point vertically. Any object hanging will automatically rotate so that its centre of gravity is aligned with that of the earth. The centre of gravity of an object is where the balance of that object lies. It’s where the maximum mass of an object or body is located. Acceleration due to gravity is the point where Earth pulls its gravitational force to attract objects towards its centre. The direction of the force of gravity is downward facing.