# momentum

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## momentum

**momentum**(mōmĕnˈtəm), in mechanics, the quantity of motion of a body, specifically the product of the mass of the body and its velocity. Momentum is a vector quantity; i.e., it has both a magnitude and a direction, the direction being the same as that of the velocity vector. When an external force acts upon a body or a system of bodies in motion, it causes a change in the momentum of the body. The impulse of a force acting on a body is the product of the force and the duration of time in which it acts and is equal to the change in momentum of the body. When no external force acts upon a body in motion or a system of bodies there is no change in the total momentum even though, as in the case of a system of bodies, there may be an internal disturbance of the system resulting in changes in the momenta of individual bodies. This conclusion is commonly known as the principle of the conservation of momentum (see conservation laws, in physics). The momentum of a body should not be confused with its kinetic energy. The distinction between them can be seen in the action of a pile driver. The distance to which the pile is driven depends upon its kinetic energy; the length of time required for the action to cease, upon its momentum. In addition to the momentum a body has because of its linear motion, the body may also have angular momentum because of rotation. The angular momentum of a particle rotating about a point is equal to the product of the mass of the particle, its angular velocity, and the square of its distance from the axis of rotation. More simply, the angular momentum is the product of the instantaneous linear momentum and the distance. Angular momentum is a vector quantity directed perpendicular to the plane of motion.

## Momentum

Linear momentum is the product of the mass and the linear velocity of a body. It is defined by Eq. (1),

*m*is the mass and

**v**is the linear velocity. Since linear momentum is the product of a scalar and a vector quantity, it is a vector and hence has both magnitude and direction.

According to the general statement of Newton's second law, for a force **F** , a momentum **P** , and a time *t*, Eq. (2) holds.

*See*Collision (physics)

When a group of bodies is subject only to forces that members of the group exert on one another, the total momentum of the group remains constant. *See* Angular momentum, Conservation of momentum, Impulse (mechanics)

## momentum

**1.**(linear momentum) Symbol:

*p.*A property of a body moving in a straight line. It is equal in magnitude to the product of the mass and velocity of the body. It is a vector quantity,

*m*, having the same direction as the velocity. See also conservation of momentum; Newton's laws of motion.

*v***2.**See angular momentum.

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.

## Momentum

a measure of mechanical motion that for a mass point is equal to the product of the mass *m* of the point and its velocity v. Momentum, *mv,* is a vector quantity, with the same direction as the velocity of the point. Upon the action of a force, the momentum of the point changes, usually both numerically and in direction. This change is determined by the second (basic) law of dynamics.

The momentum Q of a mechanical system is equal to the geometric sum of the momentums of all its points or the product of the mass *M* of the entire system and the velocity v_{c} of its center of mass: Q = Σ m_{k}v_{k} = Mv_{c}. A change in the momentum of the system takes place only through the action of external forces—that is, forces acting on the system from bodies that are not part of the system. According to the theory of the change of momentum, Q_{1} – Q_{0} = ΣS_{k}^{e}, where Q_{0} and Q_{1} are the momentums of the system at the beginning and end of a certain time interval and S_{k}^{e} are the momentums of external forces F_{k}^{e} over the time interval (this theorem is expressed in differential form by the equation *dQ/dt* = ΣF_{k}^{e}). This theorem is used for the solution of many problems in dynamics, particularly in impact theory.

For a closed system (that is, for a system that does not experience external forces), or in the case in which the geometric sum of the external forces acting on the system equals zero, the law of conservation of momentum is valid. In such cases the momentums of the individual parts of the system (for example, during the action of internal forces) may change, but in such a way that the quantity Q = Σ m_{k}v_{k} remains constant. This law explains such phenomena as jet propulsion, the recoil upon firing a gun, and the operation of a screw propeller or oars. For example, if a gun and bullet are regarded as a single system, then the pressure of the powder gases upon firing will be an internal force for the system and cannot change the momentum of the system, which was equal to zero before the firing. Therefore, in imparting the momentum m_{1}v_{1} to the bullet in the direction toward the muzzle, the powder gases simultaneously impart to the gun a momentum m_{2}v_{2}, which is numerically equal but opposite in direction, resulting in the recoil. If the velocity v_{1} of the bullet upon its exit from the barrel is known, the maximum recoil velocity v_{2} may be found from the equation m_{1}v_{1} = m_{2}v_{2} (Where v_{1} and v_{2} are scalar quantities of velocity).

At velocities close to the speed of light *c,* the momentum of a free particle is given by the formula , where *β = v/c.* When ν << *c,* this formula becomes the ordinary formula *p = mv.*

Momentum exists for physical fields (electromagnetic, gravitational, and so on). The momentum of a field is characterized by momentum density (the relationship of the momentum of a unit volume to the entire volume) and is expressed as field intensity or field potential.

S. M. TARG

## momentum

[mō′ment·əm]*m*

**v**/(1 -

*v*

^{2}/

*c*

^{2})

^{1/2}, where

*m*is the rest-mass,

**v**the velocity, and

*c*the speed of light.

## momentum

## momentum

**1.**

*Physics*the product of a body's mass and its velocity.

**2.**the impetus of a body resulting from its motion