What is centre of gravity. How is it calculated?

[chandran]

centre of mass


There is a mass at a position vector r1 from origin. like wise there are different masses at different r from the origin. the
centre of mass is the distance in which the entire mass can be concentrated at some distance R which will give the same EFFECT as that of the original
system.


What is the effect we are talking about?




What is centre of gravity.

 

[Universal]

The "effect" would be related the gravitational force. When using Newton's Law of Universal Gravitation $$F = G\frac{m_1 m_2}{r_{12}^2}$$ to calculate the force between two objects you calculate the distance between the two objects $$r_{12}$$ as the distance between the center of masses of the two objects, no matter what shape the two objects posses.

For example, when calculating the gravitational force between the Earth and moon you do the calculation by regarding the entire masses of the Earth and moon as concentrated to two single points located at the center of masses of the Earth and moon. Here the original system is the real Earth-moon system and the "concentrated" system would be considering the Earth and moon as two points with the same masses as the Earth and moon concentrated at the center of mass of the two objects and the "effect" is the gravitational force, ie. it would be the same in both situations. I hope that makes sense.

The center of gravity and center of mass is basically the same thing. Its the average location of all the mass inside an object. You can read more about at http://en.wikipedia.org/wiki/Center_of_mass .

 

[neutrino]

You can simplify matters by assuming that all mass of an object is contained at that point (centre of mass - CM) and you can evaluate the translatory motion of that object considering it as a point particle. This is what you generally do when solving problems in elementary mechanics, such as a car slowing down, a block sliding on a ramp, etc.

The centre of gravity(CG) is the nothing but the CM in a uniform gravitational field.

 

[Rade]

To Universal & Neutrino. Would your answer also apply to the three quarks found within the proton ? If not, how would one calculate the center of mass for these quarks--or is this even a valid question for a thread on Classical Physics ?

 

[neutrino]

I don't think I'm qualified to answer your question, Rade,

 

[Universal]

Rade, your question is a little beyond my knowledge. I believe that quarks are subject to all the fundamental forces, including gravity which means that they have mass. I don't know enough about quarks to know if calculating the center of mass of three quarks is a valid thing to do.

More important than gravity to quark interactions is the strong force (which involves another property called color) which is the major mediating force between quarks. The theory of quark interactions via the strong force is called Quantum Chomodynamics (QCD), and I know next to nothing about this theory. You will probably get a better answer if you asked your question in the quantum forum.