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.

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.

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 10^{10} cm. The conservation of angular momentum
(∝ ΩR^{2}) requires that as the radius decreases from 0.2 pc to
the stellar value, a factor of 10^{7}, 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
10^{4}. 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.

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.

Fr.: moment angulaire rotationnel, moment cinétique ~

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 = 4πMR^{2}/5T.

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_{s}ħ. The only values of m_{s}
(magnetic quantum number) are ± 1/2. See also
→ Stern-Gerlach experiment.