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.

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.

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.

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.

Same as → angular momentum.

→ moment; → momentum.

In → Newtonian mechanics, the momentum p of a body with → mass m and → velocity v is the product of these two quantities: p = mv. Momentum usually means → linear momentum as opposed to → angular momentum.

From L. momentum "movement, moving power," from movere "to move," → move.

Jonbâk, from jonb present stem of jonbidan "to move" (Mid.Pers. jumbidan, jumb- "to move," Lori, Laki jem "motion," related to gâm "step, pace;" O.Pers. gam- "to come; to go," Av. gam- "to come; to go," jamaiti "goes," gāman- "step, pac;" Mod.Pers. âmadan "to come;" Skt. gamati "goes;" Gk. bainein "to go, walk, step," L. venire "to come;" Tocharian A käm- "to come;" O.H.G. queman "to come;" E. come; PIE root *gwem- "to go, come") + -âk noun suffix.

1) Mechanics: The → angular momentum associated with the motion of a particle about an origin, equal to the cross product of the position vector (r) with the linear momentum (p = mv): L = r x p. Although r and p are constantly changing direction, L is a constant in the absence of any external force on the system. Also known as orbital momentum.
2) Quantum mechanics: The → angular momentum operator associated with the motion of a particle about an origin, equal to the cross product of the position vector with the linear momentum, as opposed to the → spin angular momentum. In quantum mechanics the orbital angular momentum is quantized. Its magnitude is confined to discrete values given by the expression: ħ &radic l(l + 1), where l is the orbital angular momentum quantum number, or azimuthal quantum number, and is limited to positive integral values (l = 0, 1, 2, ...). Moreover, the orientation of the direction of rotation is quantized, as determined by the → magnetic quantum number. Since the electron carries an electric charge, the circulation of electron constitutes a current loop which generates a magnetic moment associated to the orbital angular momentum.

→ orbital; → angular; → momentum.

The → angular momentum of a body rotating about an axis. The rotational angular momentum of a solid homogeneous sphere of mass M and radius R rotating about an axis passing through its center with a period of T is given by: L = 4πMR²/5T.

→ rotational; → angular; → momentum.

→ Angular momentum per unit mass.

→ specific; → angular; → momentum.

An intrinsic quantum mechanical characteristic of a particle that has no classical counterpart but may loosely be likened to the classical → angular momentum of a particle arising from rotation about its own axis. The magnitude of spin angular momentum is given by the expression S = ħ √ s(s + 1), where s is the → spin quantum number. As an example, the spin of an electron is s = 1/2; this means that its spin angular momentum is (ħ /2) √ 3 or 0.91 x 10^-34 J.s. In addition, the projection of an angular momentum onto some defined axis is also quantized, with a z-component S_z = m_sħ. The only values of m_s (magnetic quantum number) are ± 1/2. See also → Stern-Gerlach experiment.

→ spin; → angular; → momentum.

The product of the → mass loss rate and → terminal velocity used in the → radiation-driven wind theory. See also → modified wind momentum.

→ wind; → momentum.