50-547: KPAY-FM (93.9 MHz ) is a commercial radio station located in Chico, California . KPAY-FM airs a news/talk format. On August 1, 2019, the then-KFMF changed their format from mainstream rock to a simulcast of news/talk-formatted KPAY (1290 AM). The station changed its call sign to KPAY-FM on August 16, 2019. (KPAY AM is now a Fox Sports Radio affiliate.) 39°56′46″N 121°43′19″W / 39.946°N 121.722°W / 39.946; -121.722 This article about
100-784: A function of the distance to the origin with respect to time, and φ {\displaystyle \varphi } a function of the angle between the vector and the x axis. Then: d r d t = ( r ˙ cos ( φ ) − r φ ˙ sin ( φ ) , r ˙ sin ( φ ) + r φ ˙ cos ( φ ) ) , {\displaystyle {\frac {d\mathbf {r} }{dt}}=({\dot {r}}\cos(\varphi )-r{\dot {\varphi }}\sin(\varphi ),{\dot {r}}\sin(\varphi )+r{\dot {\varphi }}\cos(\varphi )),} which
150-548: A more detailed treatment of this and the above frequency ranges, see Electromagnetic spectrum . Gravitational waves are also described in Hertz. Current observations are conducted in the 30–7000 Hz range by laser interferometers like LIGO , and the nanohertz (1–1000 nHz) range by pulsar timing arrays . Future space-based detectors are planned to fill in the gap, with LISA operating from 0.1–10 mHz (with some sensitivity from 10 μHz to 100 mHz), and DECIGO in
200-530: A radio station in California is a stub . You can help Misplaced Pages by expanding it . Hertz The hertz (symbol: Hz ) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or cycle ) per second . The hertz is an SI derived unit whose formal expression in terms of SI base units is s , meaning that one hertz is one per second or
250-528: A straight line from the origin. Since radial motion leaves the angle unchanged, only the cross-radial component of linear velocity contributes to angular velocity. The angular velocity ω is the rate of change of angular position with respect to time, which can be computed from the cross-radial velocity as: ω = d ϕ d t = v ⊥ r . {\displaystyle \omega ={\frac {d\phi }{dt}}={\frac {v_{\perp }}{r}}.} Here
300-411: A vector or equivalently as a tensor . Consistent with the general definition, the spin angular velocity of a frame is defined as the orbital angular velocity of any of the three vectors (same for all) with respect to its own center of rotation. The addition of angular velocity vectors for frames is also defined by the usual vector addition (composition of linear movements), and can be useful to decompose
350-445: Is a perpendicular unit vector. In two dimensions, angular velocity is a number with plus or minus sign indicating orientation, but not pointing in a direction. The sign is conventionally taken to be positive if the radius vector turns counter-clockwise, and negative if clockwise. Angular velocity then may be termed a pseudoscalar , a numerical quantity which changes sign under a parity inversion , such as inverting one axis or switching
400-537: Is analogous to linear velocity , with angle replacing distance , with time in common. The SI unit of angular velocity is radians per second , although degrees per second (°/s) is also common. The radian is a dimensionless quantity , thus the SI units of angular velocity are dimensionally equivalent to reciprocal seconds , s , although rad/s is preferable to avoid confusion with rotation velocity in units of hertz (also equivalent to s ). The sense of angular velocity
450-706: Is conventionally specified by the right-hand rule , implying clockwise rotations (as viewed on the plane of rotation); negation (multiplication by −1) leaves the magnitude unchanged but flips the axis in the opposite direction . For example, a geostationary satellite completes one orbit per day above the equator (360 degrees per 24 hours) has angular velocity magnitude (angular speed) ω = 360°/24 h = 15°/h (or 2π rad/24 h ≈ 0.26 rad/h) and angular velocity direction (a unit vector ) parallel to Earth's rotation axis ( ω ^ = Z ^ {\displaystyle {\hat {\omega }}={\hat {Z}}} , in
500-852: Is equal to: r ˙ ( cos ( φ ) , sin ( φ ) ) + r φ ˙ ( − sin ( φ ) , cos ( φ ) ) = r ˙ r ^ + r φ ˙ φ ^ {\displaystyle {\dot {r}}(\cos(\varphi ),\sin(\varphi ))+r{\dot {\varphi }}(-\sin(\varphi ),\cos(\varphi ))={\dot {r}}{\hat {r}}+r{\dot {\varphi }}{\hat {\varphi }}} (see Unit vector in cylindrical coordinates). Knowing d r d t = v {\textstyle {\frac {d\mathbf {r} }{dt}}=\mathbf {v} } , we conclude that
550-405: Is necessary to uniquely specify the direction of the angular velocity; conventionally, the right-hand rule is used. Let the pseudovector u {\displaystyle \mathbf {u} } be the unit vector perpendicular to the plane spanned by r and v , so that the right-hand rule is satisfied (i.e. the instantaneous direction of angular displacement is counter-clockwise looking from
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#1732852437434600-449: Is not orthonormal and it is difficult to use, but now the velocity vector can be changed to the fixed frame or to the moving frame with just a change of bases. For example, changing to the mobile frame: where i ^ , j ^ , k ^ {\displaystyle {\hat {\mathbf {i} }},{\hat {\mathbf {j} }},{\hat {\mathbf {k} }}} are unit vectors for
650-550: Is positive since the satellite travels prograde with the Earth's rotation (the same direction as the rotation of Earth). ^a Geosynchronous satellites actually orbit based on a sidereal day which is 23h 56m 04s, but 24h is assumed in this example for simplicity. In the simplest case of circular motion at radius r {\displaystyle r} , with position given by the angular displacement ϕ ( t ) {\displaystyle \phi (t)} from
700-466: Is the Planck constant . The hertz is defined as one per second for periodic events. The International Committee for Weights and Measures defined the second as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium -133 atom" and then adds: "It follows that the hyperfine splitting in the ground state of
750-407: Is the direction of the angular velocity vector, and the magnitude of the angular velocity is consistent with the two-dimensional case. If we choose a reference point r 0 {\displaystyle {{\boldsymbol {r}}_{0}}} fixed in the rigid body, the velocity r ˙ {\displaystyle {\dot {\boldsymbol {r}}}} of any point in
800-404: Is then where e ˙ i = d e i d t {\displaystyle {\dot {\mathbf {e} }}_{i}={\frac {d\mathbf {e} _{i}}{dt}}} is the time rate of change of the frame vector e i , i = 1 , 2 , 3 , {\displaystyle \mathbf {e} _{i},i=1,2,3,} due to
850-452: Is usually measured in kilohertz (kHz), megahertz (MHz), or gigahertz (GHz). with the latter known as microwaves . Light is electromagnetic radiation that is even higher in frequency, and has frequencies in the range of tens of terahertz (THz, infrared ) to a few petahertz (PHz, ultraviolet ), with the visible spectrum being 400–790 THz. Electromagnetic radiation with frequencies in the low terahertz range (intermediate between those of
900-512: The angular speed (or angular frequency ), the angular rate at which the object rotates (spins or revolves). The pseudovector direction ω ^ = ω / ω {\displaystyle {\hat {\boldsymbol {\omega }}}={\boldsymbol {\omega }}/\omega } is normal to the instantaneous plane of rotation or angular displacement . There are two types of angular velocity: Angular velocity has dimension of angle per unit time; this
950-443: The geocentric coordinate system ). If angle is measured in radians, the linear velocity is the radius times the angular velocity, v = r ω {\displaystyle {\boldsymbol {v}}=r{\boldsymbol {\omega }}} . With orbital radius 42,000 km from the Earth's center, the satellite's tangential speed through space is thus v = 42,000 km × 0.26/h ≈ 11,000 km/h. The angular velocity
1000-407: The reciprocal of one second . It is used only in the case of periodic events. It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves . For high frequencies, the unit is commonly expressed in multiples : kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz). Some of the unit's most common uses are in
1050-446: The 0.1–10 Hz range. In computers, most central processing units (CPU) are labeled in terms of their clock rate expressed in megahertz ( MHz ) or gigahertz ( GHz ). This specification refers to the frequency of the CPU's master clock signal . This signal is nominally a square wave , which is an electrical voltage that switches between low and high logic levels at regular intervals. As
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#17328524374341100-468: The 1970s. In some usage, the "per second" was omitted, so that "megacycles" (Mc) was used as an abbreviation of "megacycles per second" (that is, megahertz (MHz)). Sound is a traveling longitudinal wave , which is an oscillation of pressure . Humans perceive the frequency of a sound as its pitch . Each musical note corresponds to a particular frequency. An infant's ear is able to perceive frequencies ranging from 20 Hz to 20 000 Hz ;
1150-476: The average adult human can hear sounds between 20 Hz and 16 000 Hz . The range of ultrasound , infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtohertz into the terahertz range and beyond. Electromagnetic radiation is often described by its frequency—the number of oscillations of the perpendicular electric and magnetic fields per second—expressed in hertz. Radio frequency radiation
1200-443: The body is given by Consider a rigid body rotating about a fixed point O. Construct a reference frame in the body consisting of an orthonormal set of vectors e 1 , e 2 , e 3 {\displaystyle \mathbf {e} _{1},\mathbf {e} _{2},\mathbf {e} _{3}} fixed to the body and with their common origin at O. The spin angular velocity vector of both frame and body about O
1250-449: The body. The components of the spin angular velocity pseudovector were first calculated by Leonhard Euler using his Euler angles and the use of an intermediate frame: Euler proved that the projections of the angular velocity pseudovector on each of these three axes is the derivative of its associated angle (which is equivalent to decomposing the instantaneous rotation into three instantaneous Euler rotations ). Therefore: This basis
1300-569: The caesium 133 atom is exactly 9 192 631 770 hertz , ν hfs Cs = 9 192 631 770 Hz ." The dimension of the unit hertz is 1/time (T ). Expressed in base SI units, the unit is the reciprocal second (1/s). In English, "hertz" is also used as the plural form. As an SI unit, Hz can be prefixed ; commonly used multiples are kHz (kilohertz, 10 Hz ), MHz (megahertz, 10 Hz ), GHz (gigahertz, 10 Hz ) and THz (terahertz, 10 Hz ). One hertz (i.e. one per second) simply means "one periodic event occurs per second" (where
1350-549: The cross-radial speed v ⊥ {\displaystyle v_{\perp }} is the signed magnitude of v ⊥ {\displaystyle \mathbf {v} _{\perp }} , positive for counter-clockwise motion, negative for clockwise. Taking polar coordinates for the linear velocity v {\displaystyle \mathbf {v} } gives magnitude v {\displaystyle v} (linear speed) and angle θ {\displaystyle \theta } relative to
1400-422: The description of periodic waveforms and musical tones , particularly those used in radio - and audio-related applications. It is also used to describe the clock speeds at which computers and other electronics are driven. The units are sometimes also used as a representation of the energy of a photon , via the Planck relation E = hν , where E is the photon's energy, ν is its frequency, and h
1450-440: The event being counted may be a complete cycle); 100 Hz means "one hundred periodic events occur per second", and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz , or a human heart might be said to beat at 1.2 Hz . The occurrence rate of aperiodic or stochastic events is expressed in reciprocal second or inverse second (1/s or s ) in general or, in
1500-541: The frame fixed in the moving body. This example has been made using the Z-X-Z convention for Euler angles. The angular velocity tensor is a skew-symmetric matrix defined by: The scalar elements above correspond to the angular velocity vector components ω = ( ω x , ω y , ω z ) {\displaystyle {\boldsymbol {\omega }}=(\omega _{x},\omega _{y},\omega _{z})} . This
1550-449: The hertz has become the primary unit of measurement accepted by the general populace to determine the performance of a CPU, many experts have criticized this approach, which they claim is an easily manipulable benchmark . Some processors use multiple clock cycles to perform a single operation, while others can perform multiple operations in a single cycle. For personal computers, CPU clock speeds have ranged from approximately 1 MHz in
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1600-413: The highest normally usable radio frequencies and long-wave infrared light) is often called terahertz radiation . Even higher frequencies exist, such as that of X-rays and gamma rays , which can be measured in exahertz (EHz). For historical reasons, the frequencies of light and higher frequency electromagnetic radiation are more commonly specified in terms of their wavelengths or photon energies : for
1650-454: The late 1970s ( Atari , Commodore , Apple computers ) to up to 6 GHz in IBM Power microprocessors . Various computer buses , such as the front-side bus connecting the CPU and northbridge , also operate at various frequencies in the megahertz range. Higher frequencies than the International System of Units provides prefixes for are believed to occur naturally in the frequencies of
1700-415: The linear velocity is v ( t ) = d ℓ d t = r ω ( t ) {\textstyle v(t)={\frac {d\ell }{dt}}=r\omega (t)} , so that ω = v r {\textstyle \omega ={\frac {v}{r}}} . In the general case of a particle moving in the plane, the orbital angular velocity is the rate at which
1750-514: The lowercase Greek letter omega ), also known as angular frequency vector , is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction . The magnitude of the pseudovector, ω = ‖ ω ‖ {\displaystyle \omega =\|{\boldsymbol {\omega }}\|} , represents
1800-710: The position vector relative to a chosen origin "sweeps out" angle. The diagram shows the position vector r {\displaystyle \mathbf {r} } from the origin O {\displaystyle O} to a particle P {\displaystyle P} , with its polar coordinates ( r , ϕ ) {\displaystyle (r,\phi )} . (All variables are functions of time t {\displaystyle t} .) The particle has linear velocity splitting as v = v ‖ + v ⊥ {\displaystyle \mathbf {v} =\mathbf {v} _{\|}+\mathbf {v} _{\perp }} , with
1850-811: The quantum-mechanical vibrations of massive particles, although these are not directly observable and must be inferred through other phenomena. By convention, these are typically not expressed in hertz, but in terms of the equivalent energy, which is proportional to the frequency by the factor of the Planck constant . The CJK Compatibility block in Unicode contains characters for common SI units for frequency. These are intended for compatibility with East Asian character encodings, and not for use in new documents (which would be expected to use Latin letters, e.g. "MHz"). Angular velocity In physics , angular velocity (symbol ω or ω → {\displaystyle {\vec {\omega }}} ,
1900-440: The radial component v ‖ {\displaystyle \mathbf {v} _{\|}} parallel to the radius, and the cross-radial (or tangential) component v ⊥ {\displaystyle \mathbf {v} _{\perp }} perpendicular to the radius. When there is no radial component, the particle moves around the origin in a circle; but when there is no cross-radial component, it moves in
1950-482: The radial component of the velocity is given by r ˙ {\displaystyle {\dot {r}}} , because r ^ {\displaystyle {\hat {r}}} is a radial unit vector; and the perpendicular component is given by r φ ˙ {\displaystyle r{\dot {\varphi }}} because φ ^ {\displaystyle {\hat {\varphi }}}
2000-650: The radius vector; in these terms, v ⊥ = v sin ( θ ) {\displaystyle v_{\perp }=v\sin(\theta )} , so that ω = v sin ( θ ) r . {\displaystyle \omega ={\frac {v\sin(\theta )}{r}}.} These formulas may be derived doing r = ( r cos ( φ ) , r sin ( φ ) ) {\displaystyle \mathbf {r} =(r\cos(\varphi ),r\sin(\varphi ))} , being r {\displaystyle r}
2050-535: The rotation as in a gimbal . All components of the vector can be calculated as derivatives of the parameters defining the moving frames (Euler angles or rotation matrices). As in the general case, addition is commutative: ω 1 + ω 2 = ω 2 + ω 1 {\displaystyle \omega _{1}+\omega _{2}=\omega _{2}+\omega _{1}} . By Euler's rotation theorem , any rotating frame possesses an instantaneous axis of rotation , which
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2100-407: The rotation. This formula is incompatible with the expression for orbital angular velocity as that formula defines angular velocity for a single point about O, while the formula in this section applies to a frame or rigid body. In the case of a rigid body a single ω {\displaystyle {\boldsymbol {\omega }}} has to account for the motion of all particles in
2150-544: The rules for capitalisation of a common noun ; i.e., hertz becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case. The hertz is named after the German physicist Heinrich Hertz (1857–1894), who made important scientific contributions to the study of electromagnetism . The name was established by the International Electrotechnical Commission (IEC) in 1935. It
2200-413: The specific case of radioactivity , in becquerels . Whereas 1 Hz (one per second) specifically refers to one cycle (or periodic event) per second, 1 Bq (also one per second) specifically refers to one radionuclide event per second on average. Even though frequency, angular velocity , angular frequency and radioactivity all have the dimension T , of these only frequency is expressed using
2250-402: The tangential velocity as: Given a rotating frame of three unit coordinate vectors, all the three must have the same angular speed at each instant. In such a frame, each vector may be considered as a moving particle with constant scalar radius. The rotating frame appears in the context of rigid bodies , and special tools have been developed for it: the spin angular velocity may be described as
2300-417: The top of u {\displaystyle \mathbf {u} } ). Taking polar coordinates ( r , ϕ ) {\displaystyle (r,\phi )} in this plane, as in the two-dimensional case above, one may define the orbital angular velocity vector as: where θ is the angle between r and v . In terms of the cross product, this is: From the above equation, one can recover
2350-472: The two axes. In three-dimensional space , we again have the position vector r of a moving particle. Here, orbital angular velocity is a pseudovector whose magnitude is the rate at which r sweeps out angle (in radians per unit of time), and whose direction is perpendicular to the instantaneous plane in which r sweeps out angle (i.e. the plane spanned by r and v ). However, as there are two directions perpendicular to any plane, an additional condition
2400-480: The unit hertz. Thus a disc rotating at 60 revolutions per minute (rpm) is said to have an angular velocity of 2 π rad/s and a frequency of rotation of 1 Hz . The correspondence between a frequency f with the unit hertz and an angular velocity ω with the unit radians per second is The hertz is named after Heinrich Hertz . As with every SI unit named for a person, its symbol starts with an upper case letter (Hz), but when written in full, it follows
2450-478: The x-axis, the orbital angular velocity is the rate of change of angle with respect to time: ω = d ϕ d t {\textstyle \omega ={\frac {d\phi }{dt}}} . If ϕ {\displaystyle \phi } is measured in radians , the arc-length from the positive x-axis around the circle to the particle is ℓ = r ϕ {\displaystyle \ell =r\phi } , and
2500-482: Was adopted by the General Conference on Weights and Measures (CGPM) ( Conférence générale des poids et mesures ) in 1960, replacing the previous name for the unit, "cycles per second" (cps), along with its related multiples, primarily "kilocycles per second" (kc/s) and "megacycles per second" (Mc/s), and occasionally "kilomegacycles per second" (kMc/s). The term "cycles per second" was largely replaced by "hertz" by
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