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Angular frequency
 
 
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Do not confuse with angular velocity
Angular velocity

In physics, the angular velocity is a vector quantity which specifies the angular speed, and axis about which an object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per second, degrees per hour, etc....


In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
 (specifically mechanics
Mechanics

Mechanics is the branch of physics concerned with the behaviour of physical body when subjected to forces or Displacement , and the subsequent effect of the bodies on their environment....
 and electrical engineering
Electrical engineering

Electrical engineering, sometimes referred to as electrical and electronic engineering, is a field of engineering that deals with the study and application of electricity, electronics and electromagnetism....
), angular frequency ? (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, and radian frequency) is a scalar measure of rotation rate. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity
Angular velocity

In physics, the angular velocity is a vector quantity which specifies the angular speed, and axis about which an object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per second, degrees per hour, etc....
.






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Do not confuse with angular velocity
Angular velocity

In physics, the angular velocity is a vector quantity which specifies the angular speed, and axis about which an object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per second, degrees per hour, etc....


In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
 (specifically mechanics
Mechanics

Mechanics is the branch of physics concerned with the behaviour of physical body when subjected to forces or Displacement , and the subsequent effect of the bodies on their environment....
 and electrical engineering
Electrical engineering

Electrical engineering, sometimes referred to as electrical and electronic engineering, is a field of engineering that deals with the study and application of electricity, electronics and electromagnetism....
), angular frequency ? (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, and radian frequency) is a scalar measure of rotation rate. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity
Angular velocity

In physics, the angular velocity is a vector quantity which specifies the angular speed, and axis about which an object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per second, degrees per hour, etc....
. The term angular frequency vector is sometimes used as a synonym for the vector quantity angular velocity
Angular velocity

In physics, the angular velocity is a vector quantity which specifies the angular speed, and axis about which an object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per second, degrees per hour, etc....
 .

In SI
Si

Si, si, or SI may refer to :...
 units, angular frequency is measured in radian
Radian

The radian is a unit of plane angle, equal to 180/pi Degree , or about 57.2958 degrees, or about 57?17'45?. It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level....
s per second
Second

The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....
, with dimensions s−1 since radians are dimensionless.

One revolution is equal to 2p radians, hence

where
? is the angular frequency or angular speed (measured in radians per second),
T is the period
Periodicity

Periodicity is the quality of occurring at regular intervals or periods and can occur in different contexts:In timing devices* A clock marks time at periodic intervals....
 (measured in second
Second

The second , sometimes abbreviated sec., is the name of a units of measurement of time, and is the International System of Units SI base unit of time....
s),
f is the frequency
Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
 (measured in hertz
Hertz

The hertz is a measure of frequency per unit of time, or the number of list of cycles per second. It is the SI base unit of frequency in the International System of Units , and is used worldwide in both general-purpose and scientific contexts....
),
v is the tangential velocity
Velocity

In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
 of a point about the axis of rotation (measured in metres per second
Metre per second

Metre per second is an SI derived unit of both speed and velocity , defined by distance in metres divided by time in seconds.This is the main unit of speed....
),
r is the radius
RADIUS

Remote Authentication Dial In User Service is a networking protocol that provides centralized access, authorization and accounting management for people or computers to connect and use a network service....
 of rotation (measured in metre
Metre

The metre or meter is a Unit of measurement of length. It is the SI base unit of length in the metric system and in the International System of Units , used around the world for general and scientific purposes....
s).


Angular frequency is therefore a simple multiple of ordinary frequency. However, using angular frequency is often preferable in many applications, as it avoids the excessive appearance of . In fact, it is used in many fields of physics involving periodic phenomena, such as quantum mechanics
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
 and electrodynamics.

For example:

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

Another often encountered expression when dealing with small oscillations or where damping is negligible is:

where is the spring constant is the mass of the object.

This is referred to as the natural frequency.

Angular frequency inside an LC circuit
LC circuit

An LC circuit is a variety of resonant circuit or tuned circuit and consists of an inductor, represented by the letter L, and a capacitor, represented by the letter C....
 can also be defined as the square root of the inverse of capacitance
Capacitance

In electromagnetism and electronics, capacitance is the ability of a body to hold an electrical charge.Capacitance is also a measure of the amount of electric charge stored for a given electric potential....
 (measured in farad
Farad

The farad is the SI unit of capacitance. The farad is named after the British physicist Michael Faraday....
s), times the inductance
Inductance

Inductance is the property in an electrical circuit where a change in the current flowing through that circuit induces an Electromotive force that opposes the change in current ....
 of the circuit (in henrys).

See also

  • Orders of magnitude (angular velocity)
    Orders of magnitude (angular velocity)

    This page is a progressive and labeled list of the SI angular velocity orders of magnitude, with certain examples appended to some list objects....
  • Simple harmonic motion
    Simple harmonic motion

    Simple harmonic motion is the motion of a Harmonic oscillator#Simple harmonic oscillator, a motion that is neither driven nor Damping. The motion is Periodic function - as it repeats itself at standard intervals in a specific manner - and sine wave, with constant amplitude; the acceleration of a body executing SHM is directly proportional t...


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