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

[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)?

 

[jambaugh]

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.

 

[John Mohr]

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.