Pulsation ω in AC: Why is 2π × 50 Hz = 314 s⁻¹ and not 314 Hz? Rad/s vs Hz explained

Question

Welcome and greet to you. I'm a mechanic. I have a problem. Well, in my book by F. Przeździecki "Elektrotechnika i Elektronika" I read:

..... "For a current with an industrial frequency of 50 Hz, the pulsation is:

2 * pi * 50 = 314 s-1 (s to the -1 power). So from 50 Hz I have 314 Hz. Or so???

Shouldn't it be like this: 2 * pi * 50 Hz = 314 rad / s

Or else I'll ask. This is the problem of the following equality: rad / s = 1 / s. I am asking for a factual answer.

bava · Answer

314 rad / s

krzyjak · Answer

In books, ? is often referred to as frequency. It is just often more convenient and easier to read. Although it is really angular velocity. So a quantity describing a rotary motion. In electrical engineering, it may be the speed of a voltage vector's movement in a circle. Radian ? 57 ° So a vector with an angular velocity of 314 rad / s makes a full circle revolution (2 o PI) 50 times per second.

piotr_krak · Answer

pulsacja (omega) is pulsation and frequency (f) is frequency, so if you have a book where omega is the frequency, you can use it as kindling. There is a connection between the two of omega = 2 * PI * f and we stick to it and do not mislead others.

correction:
pulsation - circular frequency.
In the SI system, the unit of a plane angle is radian.
2 * PI in radians is full motion (360 degree angle) followed by cyclic repetition. Hence the rad / s.

http://pl.wikipedia.org/wiki/Pulsacja
http://pl.wikipedia.org/wiki/Pr%C4%99dko%C5%9B%C4%87_k%C4%85towa

stomat · Answer

Oh no, it's not like that. rad / s = 1rad / s or (1 / s) * rad for 50 Hz ? = 314 rad / s not 314Hz nor 314 1 / s! Radian and full angle are two different things!

jekab · Answer

Don't confuse ? this is the speed of rotation. Just enough. In this case, rotation angle / second

piotr_krak · Answer

omega is omega does not always interpret the same for everyone for a mathematician it means the end for physics the speed of rotation for electrical engineering pulsation we are talking about current pulsation, so about electrical engineering, and we try to explain to my colleague where the unit [rad / s] came from and not how it works [1 / s]

jekab · Answer

d It's the same. How will you explain it like that .. ??

krzyjak · Answer

Of course, from a formal point of view, frequency and pulsation are two different things. But if you take any book on signal theory, you will see that the two quantities are used interchangeably. And no one has to explain it. From the point of view of harmonic signals, pulsation is also a frequency. Pulsation has the same dimension (I'm not talking about the unit) as the frequency. The frequency tells us the number of events per second. This event may be the period of the signal, i.e. the smallest unit of time, after which the signal waveform repeats in an identical manner, but it may also be an event in the form of one complete vector passage through a circle by the angle 2PI. Using the concept of pulsation is more convenient in writing. What looks better sin (?t + ? or sin (2 o ? o f o t + ? ?

stomat · Answer

rad / s is not equal to 1 / s For 50 Hz, the pulsation is 314 rad / s

jekab · Answer

There is no such equality because rad is a measure of the angle and 1 is a number. rad ? 1 Code: text Expand Select all Copy to clipboardCzy nie powinno być raczej tak: 2*pi*50 Hz = 314 rad/s  It should be like this and that means something turned 314 radians in 1 second and it means that it made 50 full turns in 1 second

Darom · Answer

1Hz = 1 / s = 1 * cycle / s = 2pi * rad / s

As my colleague, Krzyjak wrote, the pulsation record is convenient for functions describing sinusoidal and periodic waveforms (in the distribution into sinusoidal).

My colleagues have probably written everything - so I propose to close the topic.

kisses
- GIFT-

Anonymous · Answer

In electrical engineering, pulsation is associated with a sinusoidal alternating voltage.
Well, one of my colleagues wrote that it is related to rotation.
The sine function, describing the alternating voltage, is the result of the projection of a uniform circular motion onto a plane perpendicular to the circle.
Hence the number Pi as a function of sine. Pi is 3.14 radians, the measure of the angle in rotation in a circle. The full circle is cat 2Pi = 6.28 radians.
2Pi * f pulsation, is ?, i expresses the number of revolutions per second expressed in angles.
One revolution equals 2Pi = 6.28 radians. The frequency is the number of turns.
that is, the angular quantity per second is 6.28 × f radians.
Bronek

retrofood · Answer

Half doctorate already done. If someone has something new, please write to PW. I am closing the topic for now.

Pulsation ω in AC: Why is 2π × 50 Hz = 314 s⁻¹ and not 314 Hz? Rad/s vs Hz explained

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