An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

The product of → moment of inertia and → angular velocity; synonymous with moment of momentum about an axis. Angular momentum is a vector quantity; it is conserved in an isolated system.

→ angular; → momentum.

A problem encountered by the → cold dark matter model of galaxy formation. The model predicts too small systems lacking → angular momentum, in contrast to real, observed galaxies. → cusp problem; → missing dwarfs.

→ angular; → momentum; → catastrophe

The ratio J/M, where J is the → angular momentum of a → rotating black hole and M the mass of the black hole.

→ angular; → momentum; → parameter.

1) The fact that the Sun, which contains 99.9% of the mass of the → solar system, accounts for about 2% of the total → angular momentum of the solar system. The problem of outward → angular momentum transfer has been a main topic of interest for models attempting to explain the origin of the solar system.
2) More generally, in star formation studies, the question of the origin of the angular momentum of a star and the evolution of its distribution during the early history of a star. Consider a filamentary molecular cloud with a length of 10 pc and a radius of 0.2 pc, rotating about its long axis with a typical → angular velocity of Ω = 10^-15 s^-1. At a matter density of 20 cm^-3, the cloud is about 1 → solar mass. The cloud collapses to form a star with radius of 6 x 10¹⁰ cm. The conservation of angular momentum (∝ ΩR²) requires that as the radius decreases from 0.2 pc to the stellar value, a factor of 10⁷, the value of Ω must increase by 14 orders of magnitude to 10^-1 s^-1. The star's rotational velocity will be 20% the speed of light and the ratio of → centrifugal force to gravity at the equator will be about 10⁴. Observational data, however, indicate that the youngest stars are in fact rotating quite slowly, with rotational velocities of 10% of the → break-up velocity. The angular momentum problem was first studied in the context of single stars forming in isolation (L. Mestel, 1965, Quart. J. R. Astron. Soc. 6, 161). For more information see, e.g., P. Bodenheimer, 1995, ARAA 33, 199; H. Zinnecker, 2004, RevMexAA 22, 77; R. B. Larson, 2010, Rep. Prog. Phys. 73, 014901, and references therein.

→ angular; → momentum; → problem.

A process whereby in a rotating, non-solid system matter is displaced toward (→ accretion) or away from (→ mass loss) the rotation center. See also → magnetorotational instability.

→ angular; → momentum; → transfer.

Same as → angular momentum transfer.

→ angular; → momentum; → transport.

Same as → conjugate momentum.

→ canonical; → momentum.

If q_j (j = 1, 2, ...) are generalized coordinates of a classical dynamical system, and L is its Lagrangian, the momentum conjugate to q_j is p_j = ∂L/∂q. Also known as canonical momentum.

→ conjugate; → momentum.

A fundamental law of physics which states that the momentum of a → physical system does not change in the course of time if there are no external forces acting on the system. It is embodied in → Newton's first law. This principle shows that the interaction of bodies composing a → closed system leads only to an exchange in momentum between the bodies but does not affect the motion of the system as a whole. More specifically, interactions between the composing bodies do not change the velocity of the system's → center of mass.

→ conservation; → momentum.

1) The product of the strength of either of the charges in an → electric dipole and the distance separating the two charges. It is expressed in → coulomb meters. Dipole moment is a → vector quantity. Its direction is defined as toward the positive charge. In chemistry dipole moment is a quantitative measure of polarity in a molecule; the unit is the → debye.
2) The product of the strength of either of the poles in a → magnetic dipole and the distance separating the two poles. Dipole moment is a vector quantity. Its direction is defined as toward the magnetic north pole.

→ dipole; → moment.

A tensor (T_μν) related to the → Einstein tensor through → Einstein's field equations. The energy-momentum tensor depends upon the distribution of the → energy and → matter in the space.

→ energy; → momentum; → tensor.

In → Lagrangian dynamics, momenta related to → generalized coordinates. For any system with n generalized coordinates q_i (i = 1, ..., n), generalized momenta are expressed by p_i = ∂L/∂q^._i, where L is the → Lagrangian function.

→ generalized; → momentum.

The vector → impulse of the → resultant force on a particle, in any time interval, is equal in magnitude and duration to the vector change in momentum of the particle: ∫F dt = mv₂ - mv₁. The impulse-momentum principle finds its chief application in connection with forces of short duration, such as those arising in collisions or explosions. Such forces are called → impulsive forces.

→ impulse; → momentum; → principle.

The product of an object's → mass and → velocity. It is a → vector and points in the same direction as the velocity vector. Linear momentum is distinguished from → angular momentum. When there is no opportunity for confusion, usually the term momentum is used instead of linear momentum.

→ linear; → momentum.

Same as → magnetic moment.

→ magnetic; → dipole; → moment.

1) A measure of the strength of a magnet or current-carrying coil. In the case of a bar magnet it is obtained by multiplying the distance between the two magnetic poles by the average strength of the poles. Same as → magnetic dipole moment See also → dipole moment.
2) A measure of the magnetic flux set up by the gyration of an electric charge in a magnetic field.
3) In atomic and nuclear physics, → spin magnetic moment.

→ magnetic; → moment.

A quantity defined as Π = (dM/dt) v_∞ R^0.5 for a star with radius R having a wind with → terminal velocity v_∞ and a → mass loss rate dM/dt. There is a tight linear relation between the modified wind momenta and the stellar luminosities for → Population I→ O stars. See also → wind momentum.

→ modify; → wind; → momentum.

1) Physics: An expression involving the → product a → quantity, such as → force or → mass, and its perpendicular → distance from a reference point, such as → moment of force (or → torque), → moment of inertia, → moment of momentum.
2) Statistics: For a → random variable X, its nth moment about the mean is the expected value of the nth power of X, where n is a positive integer. The nth moment of the deviation of X from the mean is called the nth central moment. The first moment is the → mean, the second central moment is the → variance.
3) A short indefinite period of time.

From O.Fr. moment, from L. momentum "movement, moving power," also "instant, importance," contraction of *movimentum, from movere, → move.

Gaštâvar literally "that which makes turn, turning agent," from gašt "turning," past stem of gaštan, gardidan "to turn, to change" (Mid.Pers. vartitan; Av. varət- "to turn, revolve;" Skt. vrt- "to turn, roll," vartate "it turns round, rolls;" L. vertere "to turn;" O.H.G. werden "to become;" PIE base *wer- "to turn, bend") + âvar agent noun of âvardan "to bring; to cause, produce" (Mid.Pers. âwurtan, âvaritan; Av. ābar- "to bring; to possess," from prefix ā- + Av./O.Pers. bar- "to bear, carry," bareθre "to bear (infinitive)," bareθri "a female that bears (children), a mother;" Mod.Pers. bordan "to carry;" Skt. bharati "he carries;" Gk. pherein; L. fero "to carry").
Dam, "breath; moment; time," from Mod./Mid.Pers. damidan "to breathe, blow;" Av. dāδmainya- "blowing up," Skt. dahm- "to blow," dhámati "blows," Gk. themeros "austere, dark-looking," Lith. dumti "to blow," PIE dhem-/dhemə- "to smoke, to blow".

A measure of a force's tendency to cause a body to → rotate about a specified → axis. It is given by the force times the perpendicular → distance of the → line of action from the axis. Same as → torque

→ moment; → force.

A quantity which is a measure of the inertness of a body in rotatory motion about an axis. It is equal to the sum of the products of the masses of all particles of the body by the squares of their distances from this axis: I = Σm_ir_i², where r_i is the distance of the particle of mass m_i from the axis. Moment of inertia depends only upon the shape of the body and the arrangement of its mass with respect to the axis. For a solid sphere it is (2/5)MR². Moment of inertia is used in place of mass in problems involving rotation. Thus, the → angular momentum is Iω and → angular kinetic energy is (1/2)Iω², where ω is → angular velocity.

→ moment; → inertia.