Center of gravity

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In physics, the center of gravity (CoG) of an object is a point at which the object's mass can be assumed, for many purposes, to be concentrated. For example, if you hang an object from a string, the object's center of gravity will be directly below the string. The path of an object in orbit depends only on its center of gravity. Most astronomical objects are radially symmetric, causing both the center of gravity and the center of mass to coincide at the center of the sphere.

The center of gravity of an object is the average location of its weight. In a uniform gravitational field, it coincides with the object's center of mass. (In modern Britain the spelling centre is standard. Both spellings originated in England; center is now standard in America.)

Note that the center of gravity of a body is not a point such that the gravitational field due to that body is equal to the gravitational field if all mass were concentrated there. Such a point usually does not exist. For example, in the case of two equal bodies the center of gravity of the system would have to be (and is) midway, but gravity due to the system is not very large near that point.

Contents 1 Similarities between center of mass and center of inertia 2 Differences between center of mass and center of inertia 3 References 4 See also

Similarities between center of mass and center of inertia

In a uniform gravitational field (in other words, when the tidal force is insignificant), the center of mass and the center of gravity are at the same location.

In a radially uniform gravitational field (such as the one formed by a typical star), the center of mass and the center of gravity of a radially symmetric object (such as planets and stars) are both at the center of the sphere.

Differences between center of mass and center of inertia

• the "center of buoyancy" of an object depends only on its geometric shape, independent of its density.

• the "center of mass" of an object depends on its shape and its density

• the center of gravity of an object depends on its shape, density, and the external gravitational field.

The center of mass of a long, uniform beam (of rectangular or circular cross section) is always at the center of the beam.

In locations where Earth's gravity dominates, the center of gravity of a vertical, long, uniform beam is closer to Earth than the center of the beam (although it is still inside the beam).

In locations where Earth's gravity dominates, the center of gravity of a horizontal, long, uniform beam is further away from Earth than the center of the beam. (The CoG may be outside the beam, if the beam is long enough and narrow enough).

When we say

(Newton's second law of motion), the "a" (acceleration) referred to is the acceleration of the center of mass. The "F" (force), however, when caused by gravitational forces, depends on the center of gravity.

References

• Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.), Brooks/Cole. ISBN 0534408427.
• Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.), W. H. Freeman. ISBN 0716708094.

See also

• The barycenter is the center of mass of two objects.
• Center of massde:Schwerpunkt

es:Centro de gravedad ja:重心 pl:Środek ciężkości pt:Centro de gravidade sl:Težišče