Discussion in 'Physics & Math' started by Saint, Oct 19, 2017.
are they the same on earth surface?
Log in or Sign up to hide all adverts.
I know what a center of mass is, but I've personally never heard of a center of gravity? My guess would be that yes, they are the same.
(At least in Newtonian physics. In Einsteinian physics you probably would have to talk about the "center of energy", but "center of gravity" makes less sense there.)
how about centroid? is it center of mass too?
I don't understand your question. Is its center of mass what too?
Yes, they're the same in any uniform gravitational field.
CG/ CofG is an engineering term. (look up descriptions of aircraft flight for example).
I think the question was "Is centroid the same as centre of mass [as well as centre of gravity]".
And the answer is "Yes" (except that the term "centroid" is usually reserved for plane figures).
It seems I learn something new every day. Thanks! Please Register or Log in to view the hidden image!
Assuming a uniform density: yes, indeed it is.
Please Register or Log in to view the hidden image!
The center pf gravity of the earth is constantly in motion;
we are dealing with the center of gravity of the earth moon system,
and also the center of gravity of the earth sun system,
and to lesser extents, the center of gravity as altered by the other planets.
So, uniformity is a nice concept which has little to do with reality.
I had always thought of mass to do with inertia, so the centre of mass would be the point around which an object would spin if a force was applied to it. Whereas the centre of gravity relates to the point where an external object would be attracted by gravity. While these two points are often the same, there is the possibility of them being different.
1) Your "definition" of centre of gravity is incorrect. (Hint: A body's center of gravity is the point around which the resultant torque due to gravity forces vanishes).
2) If your "definition" were correct then (by that definition) it wouldn't be the same as centre of mass.
If you had a large asteroid like 2 balls joined by a thin bar, then the ball closer to a larger body would experience a slightly greater force from gravity than the ball further away. As the asteroid spins, the centre of gravity would shift slightly according to which ball is closer. The centre of mass would not change.
You DID notice that earlier I stated that the terms are synonymous with regard to a uniform gravitational pull, didn't you? (I.e. your example doesn't refute anything written prior).
Again, you're using "centre of gravity" incorrectly.
Here's another definition: In physics, the center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero, or the point where if a force is applied it moves in the direction of the force without rotating.
You are right for a uniform gravitational pull, a uniform gravitational field, but this occurrance does not happen in any large volume of space.
So, given the OP: are they the same on earth surface?
And my earlier post: the same in any uniform gravitational field.
You've managed to add nothing to the discussion. Well done.
(Oh, and you'd be incorrect: in a "large volume of space" gravity would be largely uniform. The only time it wouldn't be is in space AND close to another body).
Your definition of the centre of gravity results in a line through the body. I can balance an object on a point, so there would be no torque from gravity on the body. Also I can hang a body so there is no torque, but the point holding it is on the far side of the body. I prefer that the centre of gravity results in no torque and the gravitational pull from the mass on one side of the centre is equal to the gravitational pull on the other side. Also the gravitational field at the surface of the Earth is not uniform, it is decreasing as you move away from the Earth.
No, it produces a point. (It says that quite clearly).
(And note that it's not "my" definition).
Oh wait, was that not mentioned in "my" definition? I think it was: A body's center of gravity is the point around which the resultant torque due to gravity forces vanishes).
FFS. Did you think about what you wrote?
Try this: Also the gravitational field at the surface of the Earth is not uniform, it is decreasing as you move away from the Earth.
By definition if you've moved away then you're no longer on the surface.
Well, being really picky, I'm not sure the earth's gravitational field is uniform on the surface...
There can be perhaps c.0.5% variation in the strength, maybe more, as you move from place to place.
But for something the size of an aircraft the variation across its area will almost certainly be too small to measure, and thus to all intents and purposes it can be considered uniform. Please Register or Log in to view the hidden image!
And thus you'd be correct in that CoG and CoM are synonymous.
What is "gravitational pull"?
A gravitational field is uniform under 2 circumstances, as far as I can figure
1. There exists no source. Here is the reasoning: If the field is uniform, the metric field is constant. If the metric field is constant, then the curvature field vanishes (calculus). This can only mean than there exists no source.
2. In the presence of a source, the region of spacetime where the field is uniform is very small, and inversely proportional to the mass of the source.Which follows (partly) from the definition of a spacetime manifold, and can easily be argued is the converse of my first assertion
Speaking as an Earth resident that lives by the sea I notice that the sea goes up and down (roughly) every 12 hours. Assuming my house is located on a fairly rigid body (the Earth) and the sea is fairly free to attempt to maintain an equipotential surface I conclude (with potential [a scalar] being the integral of field [a vector]) that the centre of gravity of the Earth moves about as a consequence of other bodies in the Solar system (anecdotally the Moon and Sun are the major contributors to this effect). The centre of mass of the Earth is, by definition, the centre of mass of the Earth and it is generally accepted that the centre is at the centre of a (nearly) spherical body and doesn't move.
The 'centre of mass' has a definition quality about it. For example the centre of mass of the Sun is pretty close to the centre of the Sun but the centre of mass of the Solar System (I am reliably informed) can lie outside of the Sun as a result of some of the heavier planets (especially Saturn). If rpenner were moving among us we might want to look at tidal forces in some detail but he isn't. We don't want to look at the centre of mass of our galaxy or local system because no progress would be made.
if/and as we spiral toward the great attractor would the center of gravity not then precede us as we hurtle through the cosmos at an estimated 2.2 million kilometers per hour.
Separate names with a comma.