# center of mass

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Related to center of mass: moment of inertia

## center of mass,

the point at which all the massmass,
in physics, the quantity of matter in a body regardless of its volume or of any forces acting on it. The term should not be confused with weight, which is the measure of the force of gravity (see gravitation) acting on a body.
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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. The center of mass of a body need not be within the body itself; the center of mass of a ring or a hollow cylinder is located in the enclosed space, not in the object itself. Under the action of a constant force of gravity, a body suspended or balanced at its center of mass will be stable; there will be no net momentmoment,
in physics and engineering, term designating the product of a quantity and a distance (or some power of the distance) to some point associated with that quantity.
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acting on it. Sometimes a problem may be analyzed from the point of view of the center of mass of an entire system of objects, such as several colliding elementary particles or a multiple-star system. For example, the complex motions of the earth and moon about the sun become somewhat simpler when viewed from the common center of mass of the earth-moon system, located about 1,000 mi (1,600 km) below the earth's surface. It is this point that is moving in an elliptical orbit around the sun rather than the center of mass of the earth alone.

## Center of mass

That point of a material body or system of bodies which moves as though the system's total mass existed at the point and all external forces were applied at the point. The Earth-Moon system moves in the Sun's gravitational field as though both masses were located at a center of mass some 3000 mi (4700 km) from the Earth's geometric center. The function of the center-of-mass concept is to permit analysis of the motion of an entire system as distinguished from that of its individual parts.

Consider a system of mass M composed of n bodies with masses m1, m2, …, mn, and radius vectors r1, r2, …, rn measured from some common reference point. Define a point with radius vector R, such that Eq. (1) holds. Then, it is possible to derive Eq. (2),

(1) (2) an expression of Newton's second law, which states that the center of mass at R moves as though it possessed the total mass of the system and were acted upon by the total external force.

A simplification of the description of collisions can be obtained by using a coordinate system which moves with the velocity of the center of mass before collision. See Collision (physics), Rigid-body dynamics

## center of mass

(center of inertia) The point in a material system at which the total mass of the system may be regarded as being concentrated and that moves as if all external forces on the system could be reduced to a single force acting at that point. When a body has a center of gravity, which it does in a uniform gravitational field, this point coincides with the center of mass.

Two bodies, moving under the influence of their mutual gravitation, will orbit around their center of mass, which lies on the line between them. The distances, r 1 and r 2, of the bodies from this point depend on their masses, m 1 and m 2, the more massive body lying closer. For circular orbits:

r 1 /r 2 = m 2 /m 1

## Center of Mass

(or center of inertia), a geometric point whose position characterizes the distribution of mass in a body or mechanical system.

The coordinates of the center of mass are or, for a body whose mass is continuously distributed over its volume, Here, the mk are the masses of the material particles that form the system; the xk, yk, and zk are the coordinates of the particles; M = Σmk is the mass of the system; ρ is the density; and V is the volume.

In English “center of mass” and “center of gravity” are sometimes used synonymously. Strictly speaking, however, the concept of center of gravity is meaningful only for a body located in a uniform gravitational field. By contrast, the concept of center of mass is not associated with any force field and has meaning for any mechanical system. The center of mass and center of gravity of a body are located at the same point.

When a mechanical system moves, the motion of its center of mass is the same as that of a material particle that has a mass equal to the mass of the system and that is acted on by all the external forces applied to the system. Furthermore, if the motion of a mechanical system or a body is described with respect to axes that move translationally with the center of mass and for which the origin is at the center of mass, some of the equations of motion have the same form as for motion with respect to an inertial frame of reference. Because of these properties, the concept of center of mass plays an important role in the dynamics of systems and bodies.

S. M. TARG

## center of mass

[′sen·tər əv ′mas]
(mechanics)
That point of a material body or system of bodies which moves as though the system's total mass existed at the point and all external forces were applied at the point. Also known as center of inertia; centroid.

## center of gravity, center of mass

A point within a body such that, if the whole mass of the body were concentrated there, the attraction of gravity would remain the same.
References in periodicals archive ?
Pushing the blocks away from their center of mass will cause them to lose their balance and fall.
The obtained results allow us to make a conclusion on the possibility of defining the trajectory of motion of the center of mass by lower degree polynomials without controlling its velocity at the end of virtualization.
Cyclical changes in the vertical position of the body's center of mass is one such pattern and is hypothesized to increase overall energetic efficiency through the interchange of kinetic and gravitational potential energy.
Faller, A direct and sensitive method for positioning the center of mass of the dropping object at the optical centre of the enclosed corner cube in ballistic absolute gravimeters, Metrologia 41, L19-21 (2004).
a zone that includes the center of mass of the PSF and its surroundings but does not coincide with the Airy disc of the PSF in general (Figs.
Below: The gravity of a large moon will cause its host planet wobble around the center of mass of the planet moon system.
rC] is the coordinate of the center of mass of the rotation body generated by plate by rotation (Figure 1d).
With each running stride, the athlete must place his center of mass over the foot as it touches down.
For instance, one of Salmeen's recurring problems - if Olympic swimmers have problems - is a slow-moving center of mass that results from the manner in which she throws her body through the water.
Ask a Research Question: An object's center of mass is the point where the object's weight appears to be concentrated.
He lowers his center of mass to get ready for the jump.
The 1/2 [degrees] wide field, centered on NGC 6045 (with north toward upper right), shows many galaxies undergoing interactions or mergers as they swarm around the cluster's center of mass.

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