# Center of gravity

(Redirected from Centre of gravity)

In physics, the center of gravity 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 (CoG) 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.)

## 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 the 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 the 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

[itex]\mathbf{F} = m\mathbf{a}[itex]

(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.

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