On the relation between angular momentum and angular velocity

2007 ◽  
Vol 75 (1) ◽  
pp. 53-55 ◽  
Author(s):  
J. P. Silva ◽  
J. M. Tavares
Keyword(s):  
Angular Momentum ◽  
Angular Velocity

scholarly journals On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation

2020 ◽  
Vol 15 ◽  
pp. 9-14
Author(s):  
Sergey G. Fedosin
Keyword(s):  
Angular Momentum ◽  
Neutron Star ◽  
Angular Velocity ◽  
Mass Density ◽  
Nonlinear Function ◽  
Kerr Black Hole ◽  
Special Theory ◽  
Spherical Body ◽  
Theory Of Relativity ◽  
Speed Of Light

In the framework of the special theory of relativity, elementary formulas are used to derive the formula for determining the relativistic angular momentum of a rotating ideal uniform ball. The moment of inertia of such a ball turns out to be a nonlinear function of the angular velocity of rotation. Application of this formula to the neutron star PSR J1614-2230 shows that due to relativistic corrections the angular momentum of the star increases tenfold as compared to the nonrelativistic formula. For the proton and neutron star PSR J1748-2446ad the velocities of their surface’s motion are calculated, which reach the values of the order of 30% and 19% of the speed of light, respectively. Using the formula for the relativistic angular momentum of a uniform ball, it is easy to obtain the formula for the angular momentum of a thin spherical shell depending on its thickness, radius, mass density, and angular velocity of rotation. As a result, considering a spherical body consisting of a set of such shells it becomes possible to accurately determine its angular momentum as the sum of the angular momenta of all the body’s shells. Two expressions are provided for the maximum possible angular momentum of the ball based on the rotation of the ball’s surface at the speed of light and based on the condition of integrity of the gravitationally bound body at the balance of the gravitational and centripetal forces. Comparison with the results of the general theory of relativity shows the difference in angular momentum of the order of 25% for an extremal Kerr black hole.

Why only a small fraction of quasars are radio loud?

2018 ◽  
Vol 14 (S342) ◽  
pp. 201-204
Author(s):  
Xinwu Cao
Keyword(s):  
Magnetic Field ◽  
Black Hole ◽  
Angular Momentum ◽  
Angular Velocity ◽  
Strong Magnetic Field ◽  
Weak Magnetic Field ◽  
Thin Disk ◽  
Relativistic Jets ◽  
Jet Formation ◽  
The Magnetic Field

AbstractIt is still a mystery why only a small fraction of quasars contain relativistic jets. A strong magnetic field is a necessary ingredient for jet formation. Gas falls from the Bondi radius RB nearly freely to the circularization radius Rc, and a thin accretion disk is formed within Rc We suggest that the external weak magnetic field threading interstellar medium is substantially enhanced in this region, and the magnetic field at Rc can be sufficiently strong to drive outflows from the disk if the angular velocity of the gas is low at RB. In this case, the magnetic field is efficiently dragged in the disk, because most angular momentum of the disk is removed by the outflows that lead to a significantly high radial velocity. The strong magnetic field formed in this way may accelerate jets in the region near the black hole, either by the Blandford-Payne or/and Blandford-Znajek mechanisms. If the angular velocity of the circumnuclear gas is low, the field advection in the thin disk is inefficient, and it will appear as a radio-quiet (RQ) quasar.

scholarly journals Binary Orbit Perturbations and the Rotational Angular Momentum of Stellar Interiors

1970 ◽  
Vol 4 ◽  
pp. 187-192
Author(s):  
Stanley Sobieski
Keyword(s):  
Angular Momentum ◽  
Angular Velocity ◽  
Significant Variation ◽  
Eclipsing Binaries ◽  
Model Parameters ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Stellar Interiors ◽  
Binary Orbit ◽  
Photometric Variation

AbstractCalculations show that a significant variation in the minima of eclipsing binaries should arise for systems where axial precession exists. Several different angular velocity distributions are assumed in order to estimate the expected photometric variation as a function of the model parameters. It is found that the solid body rotation approximation is a reasonable representation unless interiors rotate more rapidly than present models predict.

scholarly journals Geodesics in the field of a rotating deformed gravitational source

2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641006 ◽  
Author(s):  
K. A. Boshkayev ◽  
H. Quevedo ◽  
M. S. Abutalip ◽  
Zh. A. Kalymova ◽  
Sh. S. Suleymanova
Keyword(s):  
Angular Momentum ◽  
Gravitational Field ◽  
Angular Velocity ◽  
Circular Orbits ◽  
Frame Dragging ◽  
Test Particles ◽  
Gravitational Source ◽  
Massive Particles ◽  
Analytic Expressions

We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the source on the motion of test particles. We show that the effects originating from the rotation can be balanced by the effects due to the oblateness of the source.

scholarly journals ON STABILIZATION OF UNSTABLE ROTATION IN THE RESISTING MEDIUM OF THE LAGRANGE GYROSCOPE USING THE SECOND GYROSCOPE AND ELASTIC HINGES

2021 ◽  
Vol 3 (2) ◽  
pp. 103-116
Author(s):  
Ya. Sviatenko ◽  
Keyword(s):  
Fixed Point ◽  
Angular Momentum ◽  
Angular Velocity ◽  
Elastic Recovery ◽  
Center Of Mass ◽  
Uniform Rotation ◽  
Resisting Medium ◽  
The Common ◽  
Elastic Coefficients ◽  
Kinetic Moment

The possibility of stabilizing an unstable uniform rotation in a resisting medium of a "sleeping" Lagrange gyroscope using a rotating second gyroscope and elastic spherical hinges is considered. The "sleeping" gyroscope rotates around a fixed point with an elastic recovery spherical hinge, and the second gyroscope is located above it. The gyroscopes are also connected by an elastic spherical restorative hinge and their rotation is supported by constant moments directed along their axes of rotation. It is shown that stabilization will be impossible in the absence of elasticity in the common joint and the coincidence of the center of mass of the second gyroscope with its center. With the help of the kinetic moment of the second gyroscope and the elasticity coefficients of the hinges, on the basis of an alternative approach, the stabilization conditions obtained in the form of a system of three inequalities and the conditions found on the elasticity coefficients at which the leading coefficients of these inequalities are positive. It is shown that stabilization will always be possible at a sufficiently large angular velocity of rotation of the second gyroscope under the assumption that the center of mass of the second gyroscope and the mechanical system are below the fixed point. The possibility of stabilizing the unstable uniform rotation of the "sleeping" Lagrange gyroscope using the second gyroscope and elastic spherical joints in the absence of dissipation is also considered. The "sleeping" gyroscope rotates at an angular velocity that does not meet the Mayevsky criterion. It is shown that stabilization will be impossible in the absence of elasticity in the common joint and the coincidence of the center of mass of the second gyroscope with its center. On the basis of the innovation approach, stabilization conditions were obtained in the form of a system of three irregularities using the kinetic moment of the second gyroscope and the elastic coefficients of the hinges. The condition for the angular momentum of the first gyroscope and the elastic coefficients at which the leading coefficients of these inequalities are positive are found. It is shown that if the condition for the angular momentum of the first gyroscope is fulfilled, stabilization will always be possible at a sufficiently large angular velocity of rotation of the second gyroscope, and in this case the center of mass of the second gyroscope can be located above the fixed point.

Angular Momentum of a Torque-Free Deforming Axisymmetric Gyro

1994 ◽  
Vol 61 (1) ◽  
pp. 117-123
Author(s):  
F. P. J. Rimrott ◽  
F. Janabi-Sharifi
Keyword(s):  
Angular Momentum ◽  
Angular Velocity ◽  
Large Deformation ◽  
Small Deformation ◽  
Matrix Form ◽  
Stability Studies ◽  
Attitude Stability ◽  
Small Deformations

Attitude drift and attitude stability studies of torque-free gyros involve an angular momentum that is constant in magnitude and direction. The problem is to find suitable coordinates to describe the gyro’s behavior, and then to express the (constant) angular momentum in these coordinates. Expressions for small deformation are available. In the present paper the expression, in floating coordinates, for the angular momentum of a torque-free deforming axisymmetric gyro in terms of inertia moments and angular velocity components is extended to beyond small deformations. The angular momentum expression is written first in its general form. Thqn the angular momentum is expressed in matrix form for the calculation of angular momentum components for arbitrarily large deformation. Finally, three models are presented to illustrate the application of the angular momentum expression obtained.

scholarly journals Spin angular momentum of proton spin puzzle in complex octonion spaces

2017 ◽  
Vol 14 (07) ◽  
pp. 1750102 ◽  
Author(s):  
Zi-Hua Weng
Keyword(s):  
Electromagnetic Field ◽  
Quantum Mechanics ◽  
Dipole Moment ◽  
Angular Momentum ◽  
Angular Velocity ◽  
Orbital Angular Momentum ◽  
Magnetic Dipole Moment ◽  
Proton Spin ◽  
Spin Angular Momentum ◽  
Precessional Motion

The paper focuses on considering some special precessional motions as the spin motions, separating the octonion angular momentum of a proton into six components, elucidating the proton angular momentum in the proton spin puzzle, especially the proton spin, decomposition, quarks and gluons, and polarization and so forth. Maxwell was the first to use the quaternions to study the electromagnetic fields. Subsequently the complex octonions are utilized to depict the electromagnetic field, gravitational field, and quantum mechanics and so forth. In the complex octonion space, the precessional equilibrium equation infers the angular velocity of precession. The external electromagnetic strength may induce a new precessional motion, generating a new term of angular momentum, even if the orbital angular momentum is zero. This new term of angular momentum can be regarded as the spin angular momentum, and its angular velocity of precession is different from the angular velocity of revolution. The study reveals that the angular momentum of the proton must be separated into more components than ever before. In the proton spin puzzle, the orbital angular momentum and magnetic dipole moment are independent of each other, and they should be measured and calculated respectively.

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