Torques and Angular Momentum on a System at Equilibrium in Special Relativity

Aranoff, Sanford

doi:10.1119/1.1975612

Cited by 9 publications

(4 citation statements)

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“…One assumes that a rotating system's angular momentum can be expressed by an antisymmetric four-tensor J μ ν with six independents components [25], three of them could correspond to spatial vector angular momentum.…”

Section: Relativistic Rotation Relationshipmentioning

confidence: 99%

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Relativistic mechanics and thermodynamics. III. Rotation

Güémez¹

2021

Eur. J. Phys.

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A covariant four-tensor rotation equation—for bi-dimensional composite body—, by generalising cross product to four-vectors, is obtained. From it, a relativistic angular impulse-angular momentum variation equation (Poinsot–Euler rotation equation) and its pseudo-work-rotational kinetic energy variation equation (Poinsot–Euler pseudo-work equation), are obtained for a body spinning—with constant angular momentum direction—by external torques. Two rotational processes are analysed by using this four-tensor formalism—completed by a four-vector fundamental equation (Newton’s second law and thermodynamics first law)—: a rotating body subjected to conservative and friction forces torque—a mechanical energy dissipation process—, and a device spinning by torque produced by chemical reactions—a mechanical energy production process.

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Section: Relativistic Rotation Relationshipmentioning

confidence: 99%

“…Vector M k for vectors generalization to four-vectors is a four-tensor M k μ ν whose spatial part is, precisely, M k . This is achieved by defining for force F k , the M k a b component for the fourtensor torque M k μ ν as [25]…”

Section: Relativistic Rotation Relationshipmentioning

confidence: 99%

Relativistic mechanics and thermodynamics. III. Rotation

Güémez¹

2021

Eur. J. Phys.

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“…Inspired by the relativistic electromagnetic field 4-tensor formalism, one assumes that an anti-symmetric angular momentum 4-tensor has six independents components [39], three of them could correspond to vector angular momentum three components. Given two 4-vectors, a μ = (a 1 , a 2 , a 3 , a 4 ) ≡ (a, a 4 ) -with vector a = (a 1 , a 2 , a 3 ) -and b…”

Section: Composite System Four-tensor Rotation Equationmentioning

confidence: 99%

On the relativistic lever paradox

Güémez¹

2021

Phys. Scr.

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As the 'relativistic lever paradox' is a characteristic topic in the theory of relativity application to rotation processes, a covariant four-tensor equation is developed to describe the relativistic rigidrotation of an extended body subjected to external torques, and its Lorentz transformation between frames S and S in the standard configuration is analysed, to discuss this paradox. From the four-tensor rotation equation applied to an L-shaped body submitted to several torques it is concluded that although the system does not vary its angular momentum in frame S-in which simultaneously applied forces resultant torque is zero -, in frame S, it does vary its angular momentum and exerted torque on it is non-zero. From this formalism (asynchronous formulation of relativity), in frame S, angular momentum variation is related to Einsteinʼs inertia of energy principle, and the non-zero torque is a consequence of the relativity of simultaneity, showing that this description is coherent and that there is no paradox.2 [1]. In frame S, on element 1, located at L 1 = (L 1 , 0, 0), force F 1 = (0, F 1 , 0), and on element 2, located at L 2 = (0, − L 2 , 0), force F 2 = (−F 2 , 0, 0), are applied. The pivot, located at O, RECEIVED

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“…It must be based on known prerelativistic descriptions. On the one hand, it seems necessary to maintain the classical concept that the resultant force on the body must be zero (zero total impulse) when the motion remains uniform and to assure that when no torque is applied to the system in a certain reference frame, no torque is applied to it in another frame [36]. On the other hand, in classical mechanics forces on an extended system are applied simultaneously.…”

Section: Asynchronous Formulationmentioning

confidence: 99%

Relativistic Thermodynamics: A Modern 4-Vector Approach

Güémez

2011

Physics Research International

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Using the Minkowski relativistic 4-vector formalism, based on Einstein's equation, and the relativistic thermodynamics asynchronous formulation (Grøn (1973)), the isothermal compression of an ideal gas is analyzed, considering an electromagnetic origin for forces applied to it. This treatment is similar to the description previously developed by Van Kampen (van Kampen (1969)) and Hamity (Hamity (1969)). In this relativistic framework Mechanics and Thermodynamics merge in the first law of relativistic thermodynamics expressed, using 4-vector notation, such as ΔUμ = Wμ + Qμ, in Lorentz covariant formulation, which, with the covariant formalism for electromagnetic forces, constitutes a complete Lorentz covariant formulation for classical physics.

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Torques and Angular Momentum on a System at Equilibrium in Special Relativity

Cited by 9 publications

References 0 publications

Relativistic mechanics and thermodynamics. III. Rotation

Relativistic mechanics and thermodynamics. III. Rotation

On the relativistic lever paradox

Relativistic Thermodynamics: A Modern 4-Vector Approach

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