
Review of Short Phrases and Links 
This Review contains major "Angular Momentum" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 Angular momentum is an important concept in both physics and engineering, with numerous applications.
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 Angular momentum is the quantity obtained by multiplying the moment of inertia of a body by its angular speed.
 The angular momentum is a measure for the amount of torque that has been applied over time to the object.
 Angular momentum is a pseudovector quantity because it gains an additional sign flip under an improper rotation.
 Angular momentum is defined with respect to an origin, NOT an axis of rotation.
Angular Momentum
 In modern (late 20th century) theoretical physics, angular momentum is described using a different formalism.
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 Constant angular momentum is extremely useful when dealing with the orbits of planets and satellites, and also when analyzing the Bohr model of the atom.
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 Angular momentum is important in physics because it is a conserved quantity: a system's angular momentum stays constant unless an external torque acts on it.
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 Angular momentum can also be calculated by multiplying the square of the displacement r, the mass of the particle and the angular velocity.
 All nuclei that contain odd numbers of protons or neutrons have an intrinsic magnetic moment and angular momentum.
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 It turns out that the best that one can do is to simultaneously measure both the angular momentum vector's magnitude and its component along one axis.
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 This spin angular momentum comes in units of .
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 As a consequence, the canonical angular momentum is not gauge invariant either.
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 The direction of the angular momentum vector L is always the same as that of the areal velocity vector.
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 These include bound state and scattering problems in 1D, angular momentum and spin, commutator algebra, scattering in 3D abd time dependent processes.
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 In a closed system angular momentum is constant.
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 Therefore, there are limits to what can be known or measured about a particle's angular momentum.
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 It is the same angular momentum one would obtain if there were just one particle of mass M moving at velocity V located at the center of mass.
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 It is therefore known as orbital angular momentum.
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 In d dimensions, the angular momentum will satisfy the same commutation relations as the generators of the d dimensional rotation group SO(d).
 For example, the kinetic energy stored in a massive rotating object such as a flywheel is proportional to the square of the angular momentum.
 The gaugeinvariant angular momentum, or "kinetic angular momentum" is given by It has been suggested that this article or section be merged with Potential.
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 Angular momentum can also be calculated by multiplying the square of the displacement r, the mass of the particle and the angular velocity.
 Because angular momentum is constant in the absence of external torques, the angular velocity (rotational speed) of the skater has to increase.
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 Answer: (a) The disk and ball's angular momentum is still constant, but (b) now the disk and ball's angular velocity decreases as time passes.
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 The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, degrees per hour, etc.
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 In rotational motion, power is equal to the product of the torque and the angular velocity, which may be measured in revolutions per minute or rpm.
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 The conservation of angular momentum is used extensively in analyzing what is called central force motion.
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 This is a commonly encountered form of the angular momentum operator, though not the most general one.
 Angular momentum operators usually occur when solving a problem with spherical symmetry in spherical coordinates.
 Rotational symmetry of space is related to the conservation of angular momentum as an example of Noether's theorem.
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 In quantum mechanics, angular momentum is quantized  that is, it cannot vary continuously, but only in " quantum leaps " between certain allowed values.
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 The exciton in the Aether Physics Model is the Aether (hole) and quantum angular momentum (electron in this case) pair.
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 Rotations and Angular Momentum on the Classical Mechanics page of the website of John Baez, especially Questions 1 and 2.
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 I can only take on a restricted range of values (integer or halfinteger), but the 'orientation' of the associated angular momentum is also quantized.
 The second term is the angular momentum that is the result of the particles spinning about their center of mass.
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 This gyroscope remains upright while spinning due to its angular momentum.
 Notice that twice the areal velocity times mass equals angular momentum, just as linear velocity times mass is linear momentum, i.e.
 Torque is the rate at which angular momentum is transferred in or out of the system.
 For example, an electron standing at rest has an angular momentum of .
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 Indeed for fermions the spin S and total angular momentum J are halfinteger.
 By pulling in her arms, she reduces her moment of inertia, causing her to spin faster (by the conservation of angular momentum).
Definition
 The classical definition of angular momentum as depends on six numbers: r x, r y, r z, p x, p y, and p z.
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 As seen from the definition, the derived SI units of angular momentum are newton metre seconds (Nms or kgm 2 s 1).
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 For example, an electron in an atom has orbital angular momentum, which results from the electron's motion about the nucleus, and spin angular momentum.
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 Angular momentum can only assume certain discrete values ("is quantized") in the quantum theory of atoms.
 The Bohr model gives an incorrect value for the ground state orbital angular momentum.
 The spin of an electron, combined with its orbital angular momentum, results in a magnetic dipole moment and creates a magnetic field.
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 They are classified according to their quark content, total angular momentum, parity, and various other properties such as Cparity and Gparity.
 Particle physicists are most interested in baryons with no orbital angular momentum (L = 0), as they correspond to ground states —states of minimal energy.
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 For example, the kinetic energy stored in a massive rotating object such as a flywheel is proportional to the square of the angular momentum.
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 This implies that angular momentum is a conserved quantity as long as there is no net torque applied to the particle.
 Discover the relationships between angular acceleration, moment of inertia, angular momentum and torque.
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 Mass and total angular momentum (J; equal to spin for point particles) do not change sign for the antiquarks.
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 For example, elementary particles, such as the electron, possess spin angular momentum, even though they are point particles.
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 When the gyroscope starts to spin, the vectors of angular momentum and torque are at odds with one another.
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 There is one absolute selection rule coming from angular momentum conservation, since the photon is spin 1.
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 In the Aether Physics Model a photon possesses half angular momentum due to electrons and half angular momentum due to positrons.
 Spin (quantum number S) is a vector quantity that represents the "intrinsic" angular momentum of a particle.
 The different orientations of orbital angular momentum represented by the magnetic quantum number can be visualized in terms of a vector model.
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 The direction of the angular momentum vector L is always the same as that of the areal velocity vector.
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 Consequently the spatial symmetries of atomic orbitals are completely determined by the angular momentum quantum numbers l and m.
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 This halfinteger spin angular momentum is the energy needed by the electron to set up a stable standing wave around the proton.
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 In quantum mechanics, angular momentum is quantized, i.e., is measured in indivisible units equivalent to Planck's constant divided by 2 pi.
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 Fermions and Bosons  A set of notes on fermions and bosons, including a review of angular momentum in quantum mechanics.
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 The intrinsic angular momentum of a rigid body or particle, especially a subatomic particle.
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 The algebraic theory of spin is a carbon copy of the Angular momentum in quantum mechanics theory.
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 Therefore as a payload is lifted up a space elevator, it needs to gain not only altitude but angular momentum (horizontal speed) as well.
 Photons have zero mass and zero electric charge, but they do carry energy, momentum and angular momentum.
 Angular momentum quantum numbers are positive integers beginning at zero and ending at one less than the principal quantum number (n1).
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 The angular momentum operator plays a central role in the theory of atomic physics and other quantum problems involving rotational symmetry.
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 Explicitly gaugeinvariant spin and orbital angular momentum operators of quarks and gluons are obtained.
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 But unlike orbital angular momentum the eigenvectors are not spherical harmonics.
 Angular momentum is the cross product of a displacement (a polar vector) and momentum (a polar vector), and is therefore a pseudovector.
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 Angular momentum is the cross product of the position vector r and the linear momentum p.
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 Physical examples of pseudovectors include the magnetic field, torque, vorticity, and the angular momentum.
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 The g factor is an essential value related to the magnetic moment of the subatomic particles and corrects for the precession of the angular momentum.
 In addition, as the primary angular momentum spins within the Aether it picks up elementary charge from the Aether.
 This extra angular momentum may come from photons or it may come from neutrinos existing in between Aether units.
 In classical mechanics, angular momentum is equal to the product of the angular velocity of the body and its moment of inertia around the axis of rotation.
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 We find the angular momentum L of a point particle with electric charge e held at a fixed position in the presence of a black hole with magnetic charge g.
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 The total linear momentum and the total angular momentum (both vectors) of an isolated system are also conserved quantities.
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 Rotational Motion: conservation of angular momentum, energy.
 All are particles that are somewhat like electrons: they have half a quantum unit of spin angular momentum, and do not participate in strong interactions.
 Angular momentum being a vector quantity, the principle applies as well to its direction as to its magnitude.
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 An electron bound in an atomic orbital has quantized values of angular momentum and energy.
 Vector mesons, as well as photons, W and Z bosons and gluons are spin +1 particles and have three possible values for spin angular momentum.
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 Another explanation is that as both vortices rotate at the same angular velocity and direction, the inner vortex has lost angular momentum.
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 Thus, the inner vortex 25 rotates or swirls about the axis 15 at a greater angular velocity than the outer vortex 24.
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 The most the can be known about an angular momentum vector is its magnitude and one of its three vector components, both of which are quantized in units of.
 All of these parameters are ultimately trigonometric functions of the ellipse's modular angle, or angular eccentricity.
 Fig. 82. The two directions for the orbital angular momentum vector l for the rotation of an electron about the internuclear axis of a diatomic molecule.
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 The factor of two multiplying the electron spin angular momentum comes from the fact that it is twice as effective in producing magnetic moment.
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 Proper motion: Apparent angular motion of a star on the celestial sphere, usually measured in seconds of arc per year.
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 The DOT provides extended sequences of solar images in various wavelengths with high angular resolution (0.2 arcsec).
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 Microscope: The angular magnification is given by where M o is the magnification of the objective and M e the magnification of the eyepiece.
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 For a rotating object, the linear distance covered at the circumference in a radian of rotation is the product of the radius with the angular speed.
 In the case of pure circular motion, the angular velocity is equal to linear velocity divided by the radius.
 This gravitational coupling drains kinetic energy and angular momentum from the Earth's rotation (see also, Day and Leap second).
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 Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity.
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 Longitude is the angular distance east or west from the northsouth line that passes through Greenwich, England, to a particular location.
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 The angular distance of a position on the equator east or west of the standard Greenwich meridian up to 180o east or west.
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 In three dimensions, angular displacement has a direction and a magnitude.
 Inclination: The angular distance between a satellite's orbital plane and the equator of its primary.
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 More particularly, FIG. 7 illustrates a graph of the output voltage of the angular position sensor 20 as a function of the degrees of rotation.
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 Right Ascension  Angular distance of a body along the celestial equator from the vernal equinox eastward to the point on the equator nearest the body.
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 The celestial longitude is the angular distance along the ecliptic from the vernal equinox eastward.
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 Horwitz B, Rumsey JM, Donohue BC (1998) Functional connectivity of the angular gyrus in normal reading and dyslexia.
 The vorticity of a solid rotation is twice the angular velocity vector.
 The angular gyrus in developmental dyslexia: taskspecific differences in functional connectivity within posterior cortex.
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 Angular distance (measured in the plane of the object's orbit and in the direction of its motion) from the ascending node to the perihelion point.
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 It is the angular distance of the orbital plane from the plane of reference (usually the primary's equator or the ecliptic), normally stated in degrees.
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 Azimuth: The angular position of an object measured in the observer's horizontal plane, usually from north through east.
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 Degrees (and therefore arcminutes) are used to measure declination, or angular distance north or south of the celestial equator.
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 Latitude The angular distance of a position on its meridian north or south from the equator, measured in degrees ('a vessel at 25 degrees north latitude').
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 Hanbury Brown and Twiss used the interference signal to determine the apparent angular size of Sirius, claiming excellent resolution.
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 The angular diameter of an object as seen from a given position is the diameter measured as an angle.
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 True anomaly The angular distance of a point in an orbit past the point of periapsis, measured in degrees.
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 This is called constant angular velocity (CAV) because it takes the same amount of time for a turn of the 360 degrees of the disk at all times.
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 The angular measure of an object is usually expressed in degrees, arcminutes or arcseconds.
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 The supplementary SI unit of angular measure, defined as the central angle of a circle whose subtended arc is equal to the radius of the circle.
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 Longitude is given as an angular measurement ranging from 0° at the prime meridian to +180° eastward and −180° westward.
 Lunar distance, the angular distance of the moon from the sun, a star, or a planet, employed for determining longitude by the lunar method.
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 The moon's motion across the sky can be measured in angular size: approximately 15 degrees every hour, or 15 arcseconds per second.
 Meridians connect all points are the same angular distance (Longitude) from the Prime Meridian.
 For metric SI units power is watts, torque is newton meters and angular speed is radians per second (not rpm and not revolutions per second).
 The rotational kinetic energy and the angular momentum are constants of the motion (conserved quantities) in the absence of an overall torque.
 The areal velocity vector is always perpendicular to the conical surface and is proportional to the angular momentum of the particle.
 Because angular momentum is constant in the absence of external torques, the angular velocity (rotational speed) of the skater has to increase.
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 Likewise a body with spin angular momentum will rotate around the Earth's axis only if it is subject to a torque.
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