center of gravity(redirected from centers of gravity)
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center of gravity:see center of masscenter of mass,
the point at which all the mass of a body may be considered to be concentrated in analyzing its motion. The center of mass of a sphere of uniform density coincides with the center of the sphere.
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Center of gravity
A fixed point in a material body through which the resultant force of gravitational attraction acts. The resultant of all forces or attractions produced by the Earth's gravity on a body constitutes its weight. This weight is considered to be concentrated at the center of gravity in mechanical studies of a rigid body. The location of the center of gravity for a body remains fixed in relation to the body regardless of the orientation of the body. If supported at its center of gravity, a body would remain balanced in its initial position. See Gravity, Resultant of forces
center of gravityThe point in a material body at which a single force, which is the resultant of all external forces on the body, may be considered to act. The center of gravity of a body in a uniform gravitational field coincides with the body's center of mass. A body does not possess a center of gravity, however, if the external forces are not equivalent to a single resultant force or if the resultant does not always act on the same point of the system. This situation occurs in a nonuniform gravitational field. The Moon has strictly no center of gravity although the resultant force of the Earth's gravitational attraction always passes within a few meters of the center of mass.
Center of Gravity
the geometric point through which the resultant of all gravitational forces acting on the particles of a body passes. The location of a body’s center of gravity is fixed relative to the body regardless of the body’s position in space.
It is possible for a body’s center of gravity not to coincide with any of the points of the body; a ring is an example of such a body. If a free body is suspended by a thread attached successively to different points of the body, the various directions of the thread will intersect at the body’s center of gravity. In a uniform gravitational field a body’s center of gravity coincides with its center of mass.
Suppose a body is divided into parts. If the weight pk of each part and the coordinates xk, yk, zk of each part’s center of gravity are known, then the coordinates of the center of gravity of the body as a whole can be found from the equations
In the case of a homogeneous body that has a center of symmetry—for example, a sphere, a cylinder, or a rectangular or round plate—the center of gravity is located at the center of symmetry.