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Angular frequency is a measure of how fast an object is rotating

In physics (specifically mechanics and electrical engineering), angular frequency ω (also called angular speed) is a scalar measure of rotation rate. Angular frequency 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 . Wikipedia does not have an article with this exact name. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... angular velocity File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... angular velocity File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... Mechanics is the branch of physics concerned with the motion of physical bodies, the forces that cause or limit these motions, and the forces to which bodies may, in turn, give rise. ... This article treats electronics engineering as a subfield of electrical engineering, though this is not typical use in some areas. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

In SI units, angular frequency is measured in radians per second, with dimensions T ⁻¹ since radians are dimensionless. Cover of brochure The International System of Units. ... The radian is a unit of plane angle. ... Look up second in Wiktionary, the free dictionary. ...

One revolution is equal to 2π radians, hence

where ω is the angular frequency or angular speed (measured in radians per second), T is the period (measured in seconds), f is the frequency (measured in hertz), v is the tangential velocity of a point about the axis of rotation (measured in metres per second), and r is the radius of rotation (measured in metres). The radian is a unit of plane angle. ... Look up second in Wiktionary, the free dictionary. ... Periodicity is the quality of occurring at regular intervals (e. ... Look up second in Wiktionary, the free dictionary. ... Sine waves of various frequencies; the lower waves have higher frequencies than those above. ... The hertz (symbol: Hz) is the SI unit of frequency. ... The velocity of an object is simply its speed in a particular direction. ... Metre per second (U.S. spelling: meter per second) is an SI derived unit of both speed (scalar) and velocity (vector), defined by distance in metres divided by time in seconds. ... In classical geometry, a radius of a circle or sphere is any line segment from its center to its boundary. ... metre or meter, see meter (disambiguation) A metre or meter[1] (symbol: m) is a unit of length and the current base unit of length in the International System of Units (SI). ...

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 π. In fact, it is used in many fields of physics involving periodic phenomena, such as quantum mechanics and electrodynamics. Fig. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ...

For example:

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

Another often encountered expression when dealing with small oscillations is:

where k is the spring constant and m is the mass of the object.

Angular frequency inside an LC circuit can also be defined as the inverse of the square root of the capacitance (measured in farads), times the inductance of the circuit (in henrys). LC circuits behave as electronic resonators, which are a key component in many applications such as oscillators, filters, tuners and frequency mixers. ... // Definition Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ... The farad (symbol: F) is the SI unit of capacitance. ... Inductance (or electric inductance) is a measure of the amount of magnetic flux produced for a given electric current. ... An inductor. ...

See also

• Frequency
• Radian
• Pulsation