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Related Concept Videos

Angular Momentum01:21

Angular Momentum

638
Angular momentum characterizes an object's rotational motion and is defined as the moment of its linear momentum about a specified point O. When a particle moves along a curved path in the x-y plane, the scalar formulation calculates the magnitude of its angular momentum, utilizing the moment arm (d), representing the perpendicular distance from point O to the line of action of the linear momentum. Despite being scalar in formulation, angular momentum is inherently a vector quantity. Its...
638
Angular Momentum and Principle Axes of Inertia01:09

Angular Momentum and Principle Axes of Inertia

428
The concept of angular momentum for a solid structure is illustrated as the cumulative result of the cross-product of the position vector of the mass element and the cross-product of the body's angular velocity with the position vector.
To put this equation into simpler terms, it can be reconfigured using rectangular coordinates. This involves choosing an alternative set of XYZ axes that are arbitrarily inclined with respect to the reference frame. The process of deriving the rectangular...
428
Angular Momentum about an Arbitrary Axis01:11

Angular Momentum about an Arbitrary Axis

387
Imagine a rigid body with a mass denoted as 'm', which has its center of mass at point G and is rotating around an inertial reference frame. The angular momentum at an arbitrary point P can be calculated by taking the cross product of the position vector and linear momentum vector for each individual mass element.
The velocity of a mass element comprises its translational velocity and the relative velocity instigated by the body's rotation. Substituting the velocity equation into...
387
Angular Momentum: Single Particle01:10

Angular Momentum: Single Particle

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Angular momentum is directed perpendicular to the plane of the rotation, and its magnitude depends on the choice of the origin. The perpendicular vector joining the linear momentum vector of an object to the origin is called the “lever arm.” If the lever arm and linear momentum are collinear, then the magnitude of the angular momentum is zero. Therefore, in this case, the object rotates about the origin such that it lies on the rim of the circumference defined by the lever arm...
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Principle of Angular Impulse and Momentum01:23

Principle of Angular Impulse and Momentum

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The angular impulse and momentum principle provides insights into how forces applied at a distance from an object's rotational axis influence its angular velocity. It builds upon the crucial relationship between the moment of force and angular momentum. By integrating this equation, substituting the limits for the initial and final times, a comprehensive expression representing the angular impulse and momentum principle is derived.
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Angular Momentum: Rigid Body01:11

Angular Momentum: Rigid Body

15.2K
The total angular momentum of a rigid body can be calculated using the summation of the angular momentum of all the tiny particles rotating in the same plane. Considering all the tiny particles rotating in the x-y plane, the direction of angular momentum of all such particles and that of the rigid body would be perpendicular to the plane of the rotation along the z-axis.
This calculation can get complicated when tiny particles within the rigid body are not rotating in the same plane but have...
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Related Experiment Video

Updated: Dec 22, 2025

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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The Angular Momentum Dilemma and Born-Jordan Quantization.

Maurice A de Gosson1

  • 1Faculty of Mathematics (NuHAG), University of Vienna, Wien, Austria.

Foundations of Physics
|May 2, 2020
PubMed
Summary

Born-Jordan quantization, not Weyl quantization, ensures the equivalence of Schrödinger and Heisenberg pictures. This approach resolves the angular momentum dilemma, suggesting it

Area of Science:

  • Quantum mechanics
  • Theoretical physics

Background:

  • The Schrödinger and Heisenberg pictures are fundamental formulations of quantum mechanics.
  • Weyl quantization is a standard method for quantizing classical systems.
  • The angular momentum dilemma is a known issue in quantum mechanics.

Purpose of the Study:

  • To demonstrate the necessity of Born-Jordan quantization for the equivalence of Schrödinger and Heisenberg pictures.
  • To resolve the angular momentum dilemma in quantum mechanics.
  • To explore a new phase space quantum mechanics formulation.

Main Methods:

  • Comparison of Born-Jordan quantization with Weyl quantization.
  • Analysis of the angular momentum dilemma under different quantization schemes.
  • Discussion of a redefined phase space quantum mechanics using Born-Jordan quasi-distributions.
Keywords:
Angular momentumBorn–Jordan quantizationWeyl quantization

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Main Results:

  • Born-Jordan quantization, not Weyl quantization, rigorously ensures the equivalence of Schrödinger and Heisenberg pictures.
  • The angular momentum dilemma is resolved by employing Born-Jordan quantization.
  • A new quasi-distribution associated with Born-Jordan quantization shows promise in time-frequency analysis.

Conclusions:

  • Born-Jordan quantization is argued to be the only physically correct quantization procedure.
  • This quantization method offers a solution to long-standing issues like the angular momentum dilemma.
  • The proposed phase space reformulation with Born-Jordan quasi-distributions has practical applications in signal analysis.