Radian

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Paul Quincey - One of the best experts on this subject based on the ideXlab platform.

  • Angles in the SI: treating the Radian as an independent, unhidden unit does not require the redefinition of the term frequency or the unit hertz.
    arXiv: Classical Physics, 2021
    Co-Authors: Paul Quincey
    Abstract:

    Some recent papers have argued that frequency should have the dimensions of angle/time, with the consequences that 1 Hz = $2\pi$ rad/s instead of 1 s$^{-1}$, and also that $\nu = \omega$ and $h = \hbar$. This letter puts the case that this argument redefines the quantity frequency and then draws conclusions from equations that rely on the standard definition being used. The problems that this redefinition is designed to address arise from the widespread unstated adoption of the Radian Convention, which treats the Radian as a dimensionless quantity equal to the number 1, in effect making the Radian a hidden unit. This convention is currently built-in to the SI, when it should be separable from it. The unhelpful status of angles in the SI can be remedied with minimal disruption by (1) changing the definition of the Radian from a Radian equals 1 m/m to e.g. a right angle equals $\pi/2$ Radians, and (2) acknowledging that the adoption of the Radian Convention is acceptable, when made explicit. The standard definitions of frequency and the hertz should remain unchanged.

  • Angles in the SI: treating the Radian as an independent, unhidden unit does not require the redefinition of the term “frequency” or the unit hertz
    Metrologia, 2020
    Co-Authors: Paul Quincey
    Abstract:

    Some recent papers have argued that frequency should have the dimensions of angle/time, with the consequences that 1 Hz = 2π rad/s instead of 1 s-1, and also that ν = ω and h = ħ. This letter puts the case that this argument redefines the quantity 'frequency' and then draws conclusions from equations that rely on the standard definition being used. The problems that this redefinition is designed to address arise from the widespread unstated adoption of the Radian Convention, which treats the Radian as a dimensionless quantity equal to the number 1, in effect making the Radian a 'hidden' unit. This convention is currently 'built-in' to the SI, when it should be separable from it. The unhelpful status of angles in the SI can be remedied with minimal disruption by (1) changing the definition of the Radian from 'a Radian equals 1 m/m' to e.g. 'a right angle equals π/2 Radians', and (2) acknowledging that the adoption of the Radian Convention is acceptable, when made explicit. The standard definitions of 'frequency' and the hertz should remain unchanged.

Walter Chapman - One of the best experts on this subject based on the ideXlab platform.

Nida Zahra - One of the best experts on this subject based on the ideXlab platform.

M.i. Kalinin - One of the best experts on this subject based on the ideXlab platform.

  • On the status of plane and solid angles in the International System of Units (SI)
    Metrologia, 2019
    Co-Authors: M.i. Kalinin
    Abstract:

    The article analyzes the arguments that have become the basis for the 1980 CIPM recommendations declaring plane and solid angles as dimensionless derived quantities. This decision was the result of an incorrect interpretation of mathematical relationships that connect the ratio of two lengths with the plane angle, and the ratio of area to square of length with the solid angle. The analysis of these relationships, presented in the article, showed that they determine neither the dimensions of the angles nor their units, but only the numerical values of the angles expressed in Radians and steRadians. It is shown that the series expansions of trigonometric functions sometimes used to prove the dimensionless character of the plane angle is also incorrect because in this case the trigonometric functions of two different types, independent of each other, are offen confused. It is established that the plane angle is an independent quantity and therefore should be assigned to the base quantities and its unit, the Radian, should be added to the base SI units. It is shown that the solid angle is the derived quantity of a plane angle. Its unit, the steRadian, is a coherent derived unit equal to the square Radian.

Richard M. Lueptow - One of the best experts on this subject based on the ideXlab platform.

  • Stability of Taylor–Couette flow in a finite-length cavity with radial throughflow
    Physics of Fluids, 2008
    Co-Authors: Eric Serre, Michael A. Sprague, Richard M. Lueptow
    Abstract:

    Linear stability analysis predicts that a radial throughflow in a Taylor–Couette system will alter the stability of the flow, but the underlying physics for the stabilization of the flow is unclear. We investigate the impact of radial inflow and outflow on Taylor vortex flow and wavy vortex flow in a finite-length cavity via direct numerical simulation using a three-dimensional spectral method. The numerical simulations are consistent with linear stability predictions in that radial inflow and strong radial outflow have a stabilizing effect, while weak radial outflow destabilizes the system slightly. A small radial outflow velocity enhances the strength of the Taylor vortices resulting in destabilization of the base flow, whereas strong radial outflow and radial inflow reduce vortex strength, thus stabilizing the system. The transition to wavy vortex flow is unaffected by small radial outflow, but is stabilized for radial inflow. For strong radial outflow the wavy vortex flow includes localized dislocatio...

  • stability of taylor couette flow in a finite length cavity with radial throughflow
    Physics of Fluids, 2008
    Co-Authors: Eric Serre, Michael A. Sprague, Richard M. Lueptow
    Abstract:

    Linear stability analysis predicts that a radial throughflow in a Taylor–Couette system will alter the stability of the flow, but the underlying physics for the stabilization of the flow is unclear. We investigate the impact of radial inflow and outflow on Taylor vortex flow and wavy vortex flow in a finite-length cavity via direct numerical simulation using a three-dimensional spectral method. The numerical simulations are consistent with linear stability predictions in that radial inflow and strong radial outflow have a stabilizing effect, while weak radial outflow destabilizes the system slightly. A small radial outflow velocity enhances the strength of the Taylor vortices resulting in destabilization of the base flow, whereas strong radial outflow and radial inflow reduce vortex strength, thus stabilizing the system. The transition to wavy vortex flow is unaffected by small radial outflow, but is stabilized for radial inflow. For strong radial outflow the wavy vortex flow includes localized dislocatio...