角周波数、角振動数

関: circular frequency

WordNet

the number of observations in a given statistical category (同)absolute frequency
the number of occurrences within a given time period; "the frequency of modulation was 40 cycles per second"; "the frequency of his seizures increased as he grew older" (同)frequence, oftenness
the ratio of the number of observations in a statistical category to the total number of observations (同)relative frequency
measured by an angle or by the rate of change of an angle; "angular momentum"
having angles or an angular shape (同)angulate

PrepTutorEJDIC

〈U〉しばしば起こること,頻繁 / 〈C〉頻度数,(発生・生現などの)回数 / 〈C〉振動数;周波数
かどのある,とがった / かどから成る;かどを成す;角度で測った / 骨ばった,やせこけた / (態度が)ぎこちない,堅苦しい

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2014/05/31 08:42:28」(JST)

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[Wiki en表示]

Angular frequency ω (in radians per second), is larger than frequency ν (in cycles per second, also called Hz), by a factor of 2π. This figure uses the symbol ν, rather than f to denote frequency.

In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit time (e.g., in rotation) or the rate of change of the phase of a sinusoidal waveform (e.g., in oscillations and waves), or as the rate of change of the argument of the sine function.

Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity. The term angular frequency vector is sometimes used as a synonym for the vector quantity angular velocity.^[1]

One revolution is equal to 2π radians, hence^[1]^[2]

where:

ω is the angular frequency or angular speed (measured in radians per second),

T is the period (measured in seconds),

f is the ordinary frequency (measured in hertz) (sometimes symbolised with ν).

Units

In SI units, angular frequency is normally presented in radians per second, even when it does not express a rotational value. From the perspective of dimensional analysis, the unit hertz (Hz) is also correct, but in practice it is only used for ordinary frequency f, and almost never for ω. This convention helps avoid confusion.^[3]

In digital signal processing, the angular frequency may be normalized by the sampling rate, yielding the normalized frequency.

Examples

A sphere rotating around an axis. Points farther from the axis move faster, satisfying ω=v/r.

Circular motion

In a rotating or orbiting object, there is a relation between distance from the axis, tangential speed, and the angular frequency of the rotation:

Oscillations of a spring

An object attached to a spring will oscillate. Assuming that the spring is ideal and massless with no damping then the motion will be simple and harmonic with an angular frequency given by:^[4]

where

k is the spring constant

m is the mass of the object.

ω is referred to as the natural frequency (which can sometimes be denoted as ω₀).

As the object oscillates, its acceleration can be calculated by

where x is displacement from an equilibrium position.

Using 'ordinary' revolutions-per-second frequency, this equation would be

LC circuits

The resonant angular frequency in an LC circuit equals the square root of the inverse of capacitance (C measured in farads), times the inductance of the circuit (L in henrys).^[5]

References and notes

^ ^a ^b Cummings, Karen; Halliday, David (Second Reprint: 2007). Understanding physics. New Delhi: John Wiley & Sons Inc., authorized reprint to Wiley - India. pp. 449, 484, 485, 487. ISBN 978-81-265-0882-2. Check date values in: |date= (help)(UP1)
^ Holzner, Steven (2006). Physics for Dummies. Hoboken, New Jersey: Wiley Publishing Inc. p. 201. ISBN 978-0-7645-5433-9.
^ Lerner, Lawrence S. (1996-01-01). Physics for scientists and engineers. p. 145. ISBN 978-0-86720-479-7.
^ Serway,, Raymond A.; Jewett, John W. (2006). Principles of physics - 4th Edition. Belmont, CA.: Brooks / Cole - Thomson Learning. pp. 375, 376, 385, 397. ISBN 978-0-534-46479-0.
^ Nahvi, Mahmood; Edminister, Joseph (2003). Schaum's outline of theory and problems of electric circuits. McGraw - Hill Companies (McGraw - Hill Professional). pp. 214, 216. ISBN 0-07-139307-2. (LC1)

Related Reading:

Olenick ,, Richard P.; Apostol, Tom M.; Goodstein, David L. (2007). The Mechanical Universe. New York City: Cambridge University Press. pp. 383–385, 391–395. ISBN 978-0-521-71592-8.

External links

UpToDate Contents

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English Journal

Diversity of acoustic streaming in a rectangular acoustofluidic field.

Tang Q1, Hu J2.
Ultrasonics.Ultrasonics.2015 Apr;58:27-34. doi: 10.1016/j.ultras.2014.11.015. Epub 2014 Dec 10.
Diversity of acoustic streaming field in a 2D rectangular chamber with a traveling wave and using water as the acoustic medium is numerically investigated by the finite element method. It is found that the working frequency, the vibration excitation source length, and the distance and phase differen
PMID 25541360

Creep behavior of starch-based nanocomposite films with cellulose nanofibrils.

Li M1, Li D2, Wang LJ3, Adhikari B4.
Carbohydrate polymers.Carbohydr Polym.2015 Mar 6;117:957-63. doi: 10.1016/j.carbpol.2014.10.023. Epub 2014 Oct 22.
Nanocomposite films were successfully prepared by incorporating cellulose nanofibrils (CNFs) from sugar beet pulp into plasticized starch (PS) at CNFs concentration of 5-20%. The storage (G') and loss (G″) moduli, creep and creep-recovery behavior of these films were studied. The creep behavior of
PMID 25498722

Lighten the Olympia of the Flatland: Probing and Manipulating the Photonic Properties of 2D Transition-Metal Dichalcogenides.

Zhou KG1, Zhang HL.
Small (Weinheim an der Bergstrasse, Germany).Small.2015 Feb 25. doi: 10.1002/smll.201403385. [Epub ahead of print]
Following the adventures of graphene, 2D transition metal dichalcogenides (TMDs) have recently seized part of the territory in the flatland. Branched by different components of metals and chalcogenides, the families of 2D TMDs have grown rapidly, in which the semiconductive ones have shown colorful
PMID 25711142

Japanese Journal

Collisions and Gravitational Interactions between Particles in Planetary Rings(Nonequilibrium Dynamics in Astrophysics and Materials Science)

OHTSUKI Keiji
Progress of theoretical physics. Supplement (195), 29-47, 2012-08-08
… In the case of dilute rings where collision frequency is sufficiently smaller than the orbital frequency, particles' orbits evolve through successive two-body collisions and/or gravitational encounters, and the evolution can be described by the formulation based on the three-body problem. … Collisions and gravitational interactions between particles result in angular momentum transfer in planetary rings. …
NAID 110009488982

Rheological properties of concentrated solutions of galactomannans in an ionic liquid

Horinaka Jun-ichi,Yasuda Ryosuke,Takigawa Toshikazu
Carbohydrate Polymers 89(4), 1018-1021, 2012-08
… Each galactomannan solution showed angular frequency dependence curves of the storage modulus and the loss modulus which were characteristic of a solution of entangled polymer chains. …
NAID 80022690681

Quantum Spin Pumping Mediated by Magnon

Nakata Kouki
J Phys Soc Jpn 81(6), 064717-064717-13, 2012-06-15
… Localized spins lose spin angular momentum by emitting magnons and conduction electrons flip from down to up by absorbing the momentum. … The spin relaxation torque has a resonance structure as a function of the angular frequency of the applied transverse field. …
NAID 150000103390

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★リンクテーブル★

リンク元	「角周波数」「角振動数」「circular frequency」
関連記事	「frequency」「angular」

「角周波数」

　　[★]

英: angular frequency、circular frequency
関: 角振動数

「角振動数」

　　[★]

英: angular frequency
関: 角周波数

「circular frequency」

　　[★]

角周波数

関: angular frequency

「frequency」

　　[★]

n.

しばしば起こること/状態。頻発、頻繁(⇔infrequency)
頻度。(脈拍・訪問・乗り物の運搬などの)回数
(物理)振動数、周波数。(数学・統計)度数、頻度
(生態)一定区画における種の個体数、頻度(特定の種がその区域の中の小区分の何パーセントに出現したかを示す数値)
(医)頻尿(urinary frequency)

「angular」

　　[★]

角の

関: angle、corner、horn

[UP1-1] Cummings, Karen; Halliday, David (Second Reprint: 2007). Understanding physics. New Delhi: John Wiley & Sons Inc., authorized reprint to Wiley - India. pp. 449, 484, 485, 487. ISBN 978-81-265-0882-2. Check date values in: |date= (help)(UP1)

[2] Holzner, Steven (2006). Physics for Dummies. Hoboken, New Jersey: Wiley Publishing Inc. p. 201. ISBN 978-0-7645-5433-9.

[3] Lerner, Lawrence S. (1996-01-01). Physics for scientists and engineers. p. 145. ISBN 978-0-86720-479-7.

[PoP1-4] Serway,, Raymond A.; Jewett, John W. (2006). Principles of physics - 4th Edition. Belmont, CA.: Brooks / Cole - Thomson Learning. pp. 375, 376, 385, 397. ISBN 978-0-534-46479-0.

[LC1-5] Nahvi, Mahmood; Edminister, Joseph (2003). Schaum's outline of theory and problems of electric circuits. McGraw - Hill Companies (McGraw - Hill Professional). pp. 214, 216. ISBN 0-07-139307-2. (LC1)

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案内

案内

angular frequency