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Problem in astrophysics
The angular momentum problem is a problem in astrophysics identified by Leon Mestel in 1965. It was found that the angular momentum of a protoplanetary
Angular_momentum_problem
Quantum mechanical operator related to rotational symmetry
mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays
Angular_momentum_operator
Conserved physical quantity; rotational analogue of linear momentum
Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical
Angular_momentum
Vector quantity in celestial mechanics
relative angular momentum (often denoted h → {\displaystyle {\vec {h}}} or h {\displaystyle \mathbf {h} } ) of a body is the angular momentum of that body
Specific_angular_momentum
Physics problem related to laws of motion and gravity
zero-angular-momentum three-body problem. In 2015, physicist Ana Hudomal discovered 14 new families of solutions for the equal-mass zero-angular-momentum three-body
Three-body_problem
Type of angular momentum in light
The orbital angular momentum of light (OAM) is the component of angular momentum of a light beam that is dependent on the field spatial distribution, and
Orbital angular momentum of light
Orbital_angular_momentum_of_light
Intrinsic quantum property of particles
Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms
Spin_(physics)
Concept in physics
In classical mechanics, the balance of angular momentum, also known as Euler's second law, is a fundamental law of physics stating that a torque (a twisting
Balance_of_angular_momentum
Problem that attempts to explain why cats fall on their feet
the problem is not as straightforward as its statement would suggest. The apparent contradiction with the law of conservation of angular momentum is resolved
Falling_cat_problem
Angular momentum in special and general relativity
physics, relativistic angular momentum encompasses to the mathematical formalisms and physical concepts that define angular momentum in special relativity
Relativistic_angular_momentum
Physical quantity carried in photons
The angular momentum of light is a vector quantity that expresses the amount of dynamical rotation present in the electromagnetic field of the light. While
Angular_momentum_of_light
Theory to explain slowing of a star's spin
Without considering magnetic braking, an angular momentum problem emerges where the large angular momentum of the cloud causes very high centrifugal
Magnetic_braking_(astronomy)
Comparison of a wide range of angular momenta
orders of magnitude for angular momentum, in Joule-seconds. Orders of magnitude (rotational speed) Orders of magnitude (momentum) Orders of magnitude (magnetic
Orders of magnitude (angular momentum)
Orders_of_magnitude_(angular_momentum)
Physical constant in quantum mechanics
relates the energy of a photon to its angular frequency, and the linear momentum of a particle to the angular wavenumber of its associated matter wave
Planck_constant
Vector used in astronomy
conservation laws, e.g., that of the angular momentum. The LRL vector A is a constant of motion of the Kepler problem, and is useful in describing astronomical
Laplace–Runge–Lenz_vector
Class of problems in classical mechanics
the particle is not aligned with position vector r, i.e., that the angular momentum vector L = r × m v is not zero. Every central force can produce uniform
Classical central-force problem
Classical_central-force_problem
Motion problem in classical mechanics
(in the center of mass frame). Proof: Defining the linear momentum p and the angular momentum L of the system, with respect to the center of mass, by the
Two-body_problem
Optical multiplexing technique
angular momentum multiplexing is a physical layer method for multiplexing signals carried on electromagnetic waves using the orbital angular momentum
Orbital angular momentum multiplexing
Orbital_angular_momentum_multiplexing
percent of its angular momentum, meaning that the Sun should be spinning much more rapidly. Attempts to resolve the angular momentum problem led to the temporary
History of Solar System formation and evolution hypotheses
History_of_Solar_System_formation_and_evolution_hypotheses
Type of motion
linear dynamics. The analog of linear momentum in rotational motion is angular momentum. The greater the angular momentum of the spinning object such as a
Rotation_around_a_fixed_axis
Hadron (subatomic particle) that is composed of three quarks
The total angular momentum (total angular momentum quantum number J) of a particle is therefore the combination of intrinsic angular momentum (spin) and
Baryon
Tool in symplectic geometry
conserved quantities for the action. The momentum map generalizes the classical notions of linear and angular momentum. It is an essential ingredient in various
Momentum_map
Attitude control device used in spacecraft
causes a counter-rotation proportionately through conservation of angular momentum. A reaction wheel can rotate only around its center of mass; it is
Reaction_wheel
Term from classical mechanics
conservation of angular momentum. Areal velocity is closely related to angular momentum. Any object has an orbital angular momentum about an origin,
Areal_velocity
SI derived unit of angle
in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one
Radian
Laws in physics about force and motion
of inertia, the counterpart of momentum is angular momentum, and the counterpart of force is torque. Angular momentum is calculated with respect to a
Newton's_laws_of_motion
Turning force around an axis
determines the rate of change of the body's angular momentum, 𝝉=d𝐋dt where 𝐋 is the angular momentum vector and t is time. For the motion of a point
Torque
Property of a mass in motion
In Newtonian mechanics, momentum (pl.: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and
Momentum
Special case of the two-body problem
θ d t {\displaystyle \omega \equiv {\frac {d\theta }{dt}}} and the angular momentum L = m r 2 ω {\displaystyle L=mr^{2}\omega } is conserved. For illustration
Kepler_problem
Dutch astronomer (1905–1973)
However, Kuiper's theory failed to address the angular momentum problem, simply attributing the loss of momentum to magnetic and electric fields instead of
Gerard_Kuiper
Technique in quantum mechanics for solving scattering problems
to a technique for solving scattering problems by decomposing each wave into its constituent angular-momentum components and solving using boundary conditions
Partial-wave_analysis
Attitude control device
motorized gimbals that tilt the rotor’s angular momentum. As the rotor tilts, the changing angular momentum causes a gyroscopic torque that rotates the
Control_moment_gyroscope
Coefficients in angular momentum eigenstates of quantum systems
numbers that arise in angular momentum coupling in quantum mechanics. They appear as the expansion coefficients of total angular momentum eigenstates in an
Clebsch–Gordan_coefficients
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
applied to change its angular momentum. The amount of torque needed to cause any given angular acceleration (the rate of change in angular velocity) is proportional
Moment_of_inertia
Theory in propeller or turbine physics
Screw Propeller" and NACA TM 491, "Propeller Problems"). In blade element momentum theory, angular momentum is included in the model, meaning that the wake
Blade_element_momentum_theory
Equations that describe the behavior of a physical system
Other dynamical variables like the momentum p of the object, or quantities derived from r and p like angular momentum, can be used in place of r as the
Equations_of_motion
Atom of the element hydrogen
from one discrete orbit to another. Bohr supposed that the electron's angular momentum is quantized with possible values: L = n ℏ {\displaystyle L=n\hbar
Hydrogen_atom
Subfield of astronomy
energy, planets, stars, galaxies, and the space between them. Angular momentum problem – Addresses conservation challenges in star and planet formation
Outline_of_astrophysics
Physics problem popularized by Richard Feynman
understood in terms of conservation of angular momentum: in its steady state, the amount of angular momentum carried by the incoming fluid is constant
Feynman_sprinkler
Problem in physics and astronomy
particle's mass and linear momentum, respectively. The particle's linear and angular momentum are not conserved in Euler's problem, since the two centers
Euler's_three-body_problem
angular momentum gradually, as illustrated by the binary pulsar PSR B1913+16. For binary black holes, the numerical solution of the two-body problem was
Two-body problem in general relativity
Two-body_problem_in_general_relativity
Equations of motion for viscous fluids
due to the angular acceleration of K′ with respect to K. The Navier–Stokes equations are strictly a statement of the balance of momentum. To fully describe
Navier–Stokes_equations
Periodic change in the direction of a rotation axis
applied to the body. In torque-free precession, the angular momentum is a constant, but the angular velocity vector changes orientation with time. What
Precession
Structure formed by diffuse material in orbital motion around a massive central body
jets are invoked by astronomers to do everything from getting rid of angular momentum in a forming star to reionizing the universe (in active galactic nuclei)
Accretion_disk
Rate of change of angle
In physics, angular frequency (symbol ω), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time)
Angular_frequency
Study of the effects of forces on undeformable bodies
body and its angular momentum, the scalar I is its moment of inertia, the vector ω is its angular velocity, the vector α is its angular acceleration,
Rigid_body_dynamics
Unsolved physics problem
proton's spin are the expectation values of the individual sources of angular momentum. These values depend on the renormalization scale, because their operators
Proton_spin_crisis
Ratio of magnetic moment to angular momentum
of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol γ, gamma. Its SI unit is the
Gyromagnetic_ratio
1922 physical experiment demonstrating that atomic spin is quantized
Stern–Gerlach experiment demonstrated that the spatial orientation of angular momentum is quantized. Thus an atomic-scale system was shown to have intrinsically
Stern–Gerlach_experiment
Ratio of magnetic moment and angular momentum
dimensionless quantity that characterizes the magnetic moment and angular momentum of a whole atom, a particle, or a nucleus. It is the ratio of the magnetic
G-factor_(physics)
Technique in computational quantum field theory
spins. While the problem of adding spins and internal orbital angular momenta is more complicated, it is only total angular momentum that requires interactions;
Light_front_quantization
Process whereby solar radiation causes orbiting dust grains to lose angular momentum
which solar radiation causes a dust grain orbiting a star to lose angular momentum relative to its orbit around the star. This is related to radiation
Poynting–Robertson_effect
Relativistic equation relating total energy to mass and momentum
h/2π; ω is the angular frequency; k is the wavevector, whose magnitude is the wavenumber k; and λ is the wavelength. The energy–momentum relation (1) can
Energy–momentum_relation
Function describing an electron in an atom
respectively correspond to an electron's energy, its orbital angular momentum, and its orbital angular momentum projected along a chosen axis . The orbitals with
Atomic_orbital
Concept in celestial mechanics
total energy (Hamiltonian), the linear momentum and the angular momentum of an isolated three-body system (the problem being either restricted or not) are
Jacobi_integral
Notation for conserved quantities in physics and chemistry
become the quantized values of the projection of spin, an intrinsic angular momentum quantum of the electron. In 1927 Ronald G. J. Fraser [de] demonstrated
Quantum_number
Quantum explanation of electromagnetic polarization
Moving magnet and conductor problem). Angular momentum of light Spin angular momentum of light Orbital angular momentum of light Quantum decoherence
Photon_polarization
Tensor describing energy momentum density in spacetime
this with the symmetry of the stress–energy tensor, one can show that angular momentum is also conserved: 0=(xαTμν−xμTαν),ν. When gravity is non-negligible
Stress–energy_tensor
Hypothetical particle composed of gluons
have total angular momentum J = 0 (which are either scalar or pseudo-scalar) or J = 2. Triple-gluon glueballs can have total angular momentum J = 1 (vector
Glueball
Theoretical cosmological structure
subjected to dynamical friction which causes it to lose energy and angular momentum to the dark matter particles of its host. Whether a subhalo survives
Dark_matter_halo
utilized by Julian Schwinger in 1952 to re-work out the theory of quantum angular momentum efficiently, given that map’s ease of organizing the (symmetric) representations
Jordan_map
Number assigned to each electron shell in an atom
quantum numbers for bound electrons are the total angular momentum of the orbit ℓ, the angular momentum in the z direction ℓz, and the spin s of the electron
Principal_quantum_number
Device for measuring or maintaining orientation
by tilting or rotation of the mounting, due to the conservation of angular momentum. Gyroscopes based on other operating principles also exist, such as
Gyroscope
Subatomic particle; made of equal numbers of quarks and antiquarks
another quantity of quantized angular momentum, called the orbital angular momentum (quantum number L), that is the angular momentum due to quarks orbiting each
Meson
Type of structure in atomic physics
magnetic moments associated with electron spin and the electrons' orbital angular momentum. Hyperfine structure, with energy shifts typically orders of magnitude
Hyperfine_structure
Foundational principle in quantum physics
inequality from above: σxσp≥ℏ2. Angular momentum uncertainty relation: For two orthogonal components of the total angular momentum operator of an object: σJiσJj≥ℏ2|⟨Jk⟩|
Uncertainty_principle
Statement relating differentiable symmetries to conserved quantities
rotation: from this symmetry, Noether's theorem dictates that the angular momentum of the system be conserved, as a consequence of its laws of motion
Noether's_theorem
Theorem used in quantum mechanics for angular momentum calculations
the basis of angular momentum eigenstates can be expressed as the product of two factors, one of which is independent of angular momentum orientation,
Wigner–Eckart_theorem
Study of the analytic properties of scattering amplitudes
the analytic properties of scattering as a function of angular momentum, where the angular momentum is not restricted to be an integer multiple of ħ but
Regge_theory
Compact astronomical body
with both charge and angular momentum. The simplest static black holes have mass but neither electric charge nor angular momentum. Contrary to the popular
Black_hole
Equation giving the form of a central force
} . Define the specific angular momentum as h = L / m {\displaystyle h=L/m} where L {\displaystyle L} is the angular momentum and m {\displaystyle m}
Binet_equation
Theory of motion and forces for objects close to the speed of light
angular momentum tensor is sometimes called a bivector because in the 3D viewpoint it is two vectors (one of these, the conventional angular momentum
Relativistic_mechanics
Type of radioactive decay
the problem of how to account for the variability of energy in known beta decay products, as well as for conservation of momentum and angular momentum in
Beta_decay
Conjecture in general relativity
disperse over time, while the parameters of the black hole (mass, angular momentum and charge) settle down to some new values. The stability of the Schwarzschild
Black hole stability conjecture
Black_hole_stability_conjecture
Backward momentum of a gun when it is discharged
barrel axis "up" from its orientation at ignition (aim angle). The angular momentum of the gun is found by integrating this equation to obtain: I d θ d
Recoil
Branch of physics
linear momentum and angular momentum. The reversal of angular momentum means reversal of both polarization state and orbital angular momentum. Reversal
Nonlinear_optics
Physical property
theory uses both axial and angular momentum balances to determine the flow and the resulting forces at the blade. The momentum equations for the far field
Wind-turbine_aerodynamics
force term. This may even include antisymmetric stresses (inputs of angular momentum), in contrast to the usually symmetrical internal contributions to
Cauchy_momentum_equation
Description of physical properties at the atomic and subatomic scale
bound states that are quantized to discrete values of energy, momentum, angular momentum, and other quantities, in contrast to classical systems where
Quantum_mechanics
System consisting of two black holes in close orbit around each other
orbit shrinking due to the emission of gravitational waves, extra angular momentum may be lost due to interactions with other matter present, such as
Binary_black_hole
Black holes are characterized only by mass, charge, and spin
three independent externally observable classical parameters: mass, angular momentum, and electric charge.[citation needed] Other characteristics (such
No-hair_theorem
Coefficients coupled with angular momentum
coefficients for the purpose of adding angular momenta. While the two approaches address exactly the same physical problem, the 3-j symbols do so more symmetrically
3-j_symbol
description of angular momentum, for example in atomic theory. The coefficients appear when there are three sources of angular momentum in the problem. For example
Racah_W-coefficient
Laws describing planetary orbits
time Gravity Kepler orbit Kepler problem Kepler's equation Laplace–Runge–Lenz vector Specific relative angular momentum, relatively easy derivation of Kepler's
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
Kepler orbit with an eccentricity of less than one
central force, the angular momentum is constant: 𝐋˙=𝐫×𝐅=𝐫×F(r)𝐫̂=0 At the closest and furthest approaches, the angular momentum is perpendicular to
Elliptic_orbit
Description of large objects' physics
provide extensions to Newton's laws in this area. The concepts of angular momentum rely on the same calculus used to describe one-dimensional motion.
Classical_mechanics
Problem in physics and celestial mechanics
the total angular momentum being constant 𝐀=∑i=1n𝐪i×𝐩i, where × is the cross product. The three components of the total angular momentum A yield three
N-body_problem
Atomic model introduced by Niels Bohr in 1913
measurement of the photon angular momentum, the law of conservation of angular momentum predicts that the angular momentum of an electron on a stationary
Bohr_model
Region outside of a rotating black hole's event horizon
extends to a greater radius at the equator. A black hole with modest angular momentum has an ergosphere with a shape approximated by an oblate spheroid,
Ergosphere
Notation in quantum physics
symbol is an abbreviated description of the spin, orbital and total angular momentum quantum numbers of the electrons in a multi-electron atom. So while
Term_symbol
Physical quantity that changes sign with improper rotation
include angular velocity, angular acceleration, angular momentum, torque, magnetic field, and magnetic dipole moment. Consider the pseudovector angular momentum
Pseudovector
Conjecture in physics
by sending a particle of angular momentum ℓ = 2 M e {\displaystyle \ell =2Me} . Because this particle has angular momentum, it can only be captured by
Cosmic_censorship_hypothesis
Vector describing a wave; often its propagation direction
related vector is the angular wave vector (or angular wavevector), with a typical unit being radian per metre. The wave vector and angular wave vector are related
Wave_vector
Measurement of viscosity in fluid dynamics
(rvθ)2 should decrease anywhere in the interval. Since |rvθ| represents angular momentum per unit mass, of a fluid element about the axis of rotation, an alternative
Taylor–Couette_flow
Cartesian vectors of position and velocity of an orbiting body in space
barycenter and total angular momentum of the Solar System (in particular the ICRF), or even a spacecraft's own orbital plane and angular momentum. The position
Orbital_state_vectors
Predecessor to modern quantum mechanics (1900–1925)
be solved. For a fixed value of the total angular momentum L, the Hamiltonian for a classical Kepler problem is (the unit of mass and unit of energy redefined
Old_quantum_theory
University Press. ISBN 978-0-521-57507-2. A. Halpern (1988). 3000 Solved Problems in Physics, Schaum Series. Mc Graw Hill. ISBN 978-0-07-025734-4. R. G.
List of equations in quantum mechanics
List_of_equations_in_quantum_mechanics
Excited atomic quantum state with high principal quantum number (n)
shows some of the energy levels of the lowest three values of orbital angular momentum in lithium. The existence of the Rydberg series was first demonstrated
Rydberg_atom
Method for specifying point positions
Positioning System and other satellite navigation systems. Absolute angular momentum Alphanumeric grid Axes conventions in engineering Celestial coordinate
Coordinate_system
Shape taken by a self-gravitating fluid body rotating at constant velocity
a^{2})-R_{J}(a^{2},b^{2},c^{2},b^{2})]=c^{2}R_{J}(a^{2},b^{2},c^{2},c^{2}).} The angular momentum L {\displaystyle L} of the Jacobi ellipsoid is given by L G M 3 r =
Jacobi_ellipsoid
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