# Technique to find CG seems like should be for C.M. instead

• I
• John Mohr
In summary, the "plumb line method" assumes the Earth's gravitational field is more or less uniform, but when in fact, technically, the gravitational field is not truly uniform regardless of the size of an object.

#### John Mohr

When thinking over the method of finding the centre of gravity that Julius Sumner Miller shows in this classic video, I wondered about if it would work in some other extreme situations.

Imagine a uniform, continuous plank of length equal to 1 Earth radii positioned at the surface of the Earth. It would seem in this case that the CG would be closer to the Earth than the C.M. (because the end closer to the Earth is within a zone where the gravitation field strength is the strongest).

And if one were to employ the classic technique used to find the "centre of gravity" by turning it around and letting a plumb line hang down, the line would all intersect at the halfway point on the plank. Would this then not be the centre of mass and not the centre of gravity (which would be off-centre and closer to the Earth)?

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Note one issue is that given you are working on a scale where you cannot treat the Earth's gravitation as uniform, you will find that the center of gravity changes as you change the orientation and position of the plank. This is because the gravity changes from position to position and does so in a non-linear way.

And as to the technique, once you are dealing with non-uniform gravitational fields all bets are off which you seem to have already reasoned out here.

Thank you for the response jambaugh. I think I follow what you were mentioning.

Would it be true to say that the "plumb line method" assumes the Earth's gravitational field is more or less uniform when dealing with small objects near the surface of the Earth? When in fact, technically, the gravitational field is not truly uniform regardless of the size of an object - just very, very small differences.

## 1. What is the difference between CG and C.M.?

CG stands for center of gravity, while C.M. stands for center of mass. While these terms are often used interchangeably, they actually have slightly different meanings. The center of gravity refers to the point at which an object's weight is evenly balanced, while the center of mass refers to the point at which an object's mass is evenly distributed.

## 2. Why is it important to find the center of gravity?

Knowing the center of gravity of an object is important for understanding its stability and balance. It can also be useful for designing structures and vehicles, as well as for predicting how objects will move and behave.

## 3. What is the technique for finding the center of gravity?

The technique for finding the center of gravity involves suspending or balancing the object in different orientations and measuring the points at which it remains balanced. The center of gravity will be located at the intersection of these points.

## 4. Can the same technique be used to find both CG and C.M.?

Yes, the technique for finding the center of gravity can also be used to find the center of mass. This is because, in most cases, an object's mass and weight are directly proportional to each other.

## 5. Are there any limitations to this technique for finding CG and C.M.?

While the technique for finding the center of gravity is generally accurate, there are some limitations to consider. It may not work for irregularly shaped objects or those with varying densities. Additionally, external forces such as air resistance or friction may affect the accuracy of the measurements.