Question

Is there any laws or explanations for center of gravity? Is there any explanation given by any Scientists for their existence and behavior?

Answer 1

You get center of gravity by using the law of gravity on each small part of a body,
and then adding the effect of all those parts up. it just comes out of the math of the law of gravity.

Answer 2

If you take a one dimensional object of mass M and place it arbitrarily on a narrow pin you will most like find that it will tip off the pin. If you move it around you may fin that it will become less tippy . Eventually you may find that it will balance at a certain point and not tip at all. You have found the locus of what is know as the center of mass or center of gravity. That locus being a line directly above the pivot point. This is the point where the moment of gravitational force of each part of the object on one side of the pin is balanced by a corresponding moment on the opposite side of the pin.
Thus for every part of mass m1 on one side at a distance x1 from the pivot point there is another mass m2 at a distance x2 that balances m1's moment in otherwords

m1*x1=m2*x2

But the moment of the whole about some arbitrary point,say Xcm, equal the sum of the moments of the parts about that point that is

M*Xcm = sum( mi*si) or Xcm= sum(mi*si)/M where si = xi+Xcm

Thus we started with a principle of moment of gravitational force about a point and an observation of equal moments is opposite directions balance i.e. do not cause rotation (tipping) and apply a little math to extend the moment to any arbitrary point.

Answer 3

@beccamarx19 what are you talking about? @Miracrown and @gleem your explanations are good and I also have my own theories for COG, but my question is, like Newton's laws of motion, is there any firm laws given for the understanding and applications of COG? you know, like any scientists and such?

Answer 4

@beccamarx19 Please don't just copy and paste info from others websites, like you have done above ^ - from here: http://www.explainthatstuff.com/center-of-gravity.html

That's against the ''os coc"... please restrain from doing such in future. Thank you.

Answer 5

@Abishek

I am not really sure what your question means.

There is no 'court of physics' which sets the laws.

The 'Laws' are merely man made explanations of observable phenomena. The more they stand up to experimental test, and the more they aid in prediction of behaviour the more 'accepted' or 'true' they become.

The validation of a law by any particular scientist, body or religion does not make it any more significant - the physics would still behave the same way in the absence of mankind's attempts to measure it.

If any one repeatable verifiable instance of the law 'failing' is detected, then the law is no longer valid (it may very well still be an extremely good approximation under a limited range of conditions)

The 'law' of centre of gravity is derived from some very simple mathematics (some of which is given by responders above). It is precisely valid for engineering calculations and has not been demonstrated to be false under normal circumstances that I am aware of.

What else do you want for an explanation?

Answer 6

@MrNood I understand your "insight" about laws of physics and from reading from the other member's responses, I understand that you calculate the COG of an object simply by adding small parts into big parts for the total calculation, as said by @Miracrown.

This is all just simple ways for doing stuff... you know? We are able to easily calculate the COG of simple objects such as a match box to mega structures as in buildings and air planes.

But, when the standard calculation of small parts of the body vary, for example, we have a non-homogeneous mixture of elements in liquid state freely floating in space... not inside the Earth's gravitational field that is, can the standard solution for explaining COG of such similar complex objects hold?

If I am not clear in this, please call me an idiot and I will follow...

Answer 7

First - all gravitational fields extend indefinitely. (it's just htat they become VERY weka at extended distances) . Do you mean 'in orbit', or 'free fall'?

I understand that the concept of gravitational attraction is good for all Newtonian physice - i.e. I do no know what happens when you get to the very micro sub atomic scale.

A liquid 'blob' floating in free spce is likely to have a very ill defined shape, hence its CoG will change as its shape changes. At any one instant I cannot see why the method of summing the mass/position factors of each small part (molecule?) would not produce a valid result for the Cof G AT THAT PRECISE INSTANT. (I can't see how you could measure it though)

Answer 8

Actually, a clump of moving matter will maintain its CoG as long as the forces acting on it that are changing the distribution are internal forces. This is a consequence of the conservation of momentum. The usual example of this effect is the explosion of an artillery shell. The CoG of the shell follows the same trajectory of the unexploded shell even after the detonation. Even a liquid or handful of rocks tossed (assuming no significant external forces as air resistance) will maintain its CoG after they are released.

Answer 9

Can you guys excuse me for some time? My brain hurts...

Answer 10

Thank you guys for looking into this matter... I have a feeling that we are missing something right under our nose...