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Difference between Center of Mass and Center of Gravity

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  • Last Updated : 23 May, 2022
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Physics has always been a fascinating topic to study. Some of the interesting issues to study include gravity, inertia, distance, displacement, and so on. Science is a comprehensive area that studies various systems such as the human body, the solar system, plant and animal tissue, chemicals, and so on. The center of mass and the center of gravity are two notions that come up frequently in physics. The distinction between the center of mass and the center of gravity will be explained in this article. The major distinction between Center of Gravity and Center of Mass is that the center of gravity is the position at which the entire body weight is balanced, while the center of mass is the position at which the entire mass of the body is directed.

COM-vs-COG

What is the Center of Mass?

The center of mass is defined as the point at which the mass’s relative position is calculated to be zero. The mass distribution is considered uniform around the center of mass. Because the center of mass is independent of the gravitational field (g), the body remains unaffected by changes in the gravitational field’s force. 

In simple rigid objects with uniform density, the center of mass is located at the center or centroid. In the case of sophisticated objects, the total center of mass becomes zero.

What is the Center of Gravity?

The center of gravity is defined as the exact place in a body around which the instants due to gravity are regarded as zero. The center of gravity is the point at which the entire body is perfectly balanced in relation to gravity. 

If that exact place is given support in the opposite direction of gravity, the body will achieve equilibrium. The center of gravity is abbreviated as C.G. or simply G. The object’s center of gravity could be inside or outside the object’s body. The gravitational field (g) always affects the center of gravity because when the gravitational field’s value varies, the center of gravity’s value changes as well.

Difference Between Center of Mass and Center of Gravity

Center of Mass

Center of Gravity

The center of mass is the point where mass distribution is uniform in all directions. The center of gravity is the point where weight is evenly distributed in all directions.
The Center of mass is based on the mass of the body. The Center of gravity is based on the weight of the body.
It is said to be the center where the entire bodily mass is concentrated. It is defined as the point at which the body’s entire weight is suspended.
There is a uniform distribution of mass of the body. There is a uniform distribution of the weight of the body.
When a body travels through an axis, the mass operating on the left side is equal to the mass acting on the right side. When a body travels through an axis, the weight on the left side becomes equal to the weight on the right side.
The change in the gravitational field has no effect on it. Changes in the force of the earth’s acting gravity usually cause the object to move closer to the parts of the object in a stronger field.
When spinning around that point, it provides some angular momentum. Because of gravity, the net torque is zero.

Solved Problems

Problem 1: Two-point masses of 3 kg and 5 kg are located at 4 m and 8 m on X-axis. Find the center of mass.

Solution:

Given,

m1 = 3 kg

m2 = 5 kg

x1 = 4 m

x2 = 8m

Using Center of mass formula,

Xcm = m1x1+m2x2/ m1+m2

= (3)(4) + (5)(8)/ 3 + 5

= 6.5

So, the center of mass is 6.5 m.

Problem 2: Two-point masses of 2 kg and 5 kg are located at 10 m and -5 m on Y-axis respectively. Calculate the center of mass.

Solution:

Given,

m1 = 2 kg

m2 = 5 kg

y1 = 10 m

y2 = -5 m

Using center of mass formula,

Ycm = m1y1+m2y2/m1+m2

= (2)(10)+(5)(-5)/2+5

= 5/7

So, the center of mass is 5/7 m.

Problem 3: In a human body, where is the center of gravity?

Solution:

The center of gravity is roughly anterior to the second sacral vertebra in anatomical location. However, because humans do not remain in the same anatomical posture for long periods of time, the precise location of the COG changes with each new position of the torso and limbs.

Problem 4: What effect does the Center of Gravity have on the balance?

Solution:

The stability of objects is affected by their center of gravity. The lower the object’s center of gravity (G), the more stable it is. The higher the thing, the more probable it is to collapse over if pushed. Racing automobiles have low centrer of gravity, allowing them to turn quickly without tipping over.

Problem 5: What is the significance of the center of gravity?

Solution:

The center of gravity greatly simplifies gravitational and dynamical calculations by treating an object’s mass as though it were concentrated at one spot.

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