# Calculation of Angular Frequency

1. Dec 19, 2011

Hi everyone,

I need to calculate the Angular frequency based on the input angular speed.
I'm thinking the formula would be

Angular Speed, ω = 2∏f
=> Angular Frequency, f = ω/2∏ = ω/360°

so, does the formula "f = ω/360°" will give me correct solution.

2. Dec 19, 2011

### gsal

No....do not use degrees...you need to leave 2.pi in radians...in other words, you just performed some kind of bad conversion...is 2.pi = 360? is it? No, it is not. 2x3.14=6.28!

3. Dec 19, 2011

But, my input angular speed is in Deg/sec....
so, you say, i convert that deg/sec to radian/sec and then use the formual f = ω/2∏ ??

4. Dec 19, 2011

### gsal

oh...that's weird.

Then, yes, convert deg/s to rad/s, first and then...

5. Dec 19, 2011

I'm little confused :(

Is in't the same thing ?

Lets say,

1. Angular Velocity = 10deg/sec
2. Convert it to radians/sec --> 10*(∏/180)
3. Now, calculate the angular frequency, f = ((10*∏)/180)/2∏
4. If we see in the above equation, ∏ in the neumarator and ∏ in the denominator will be cancelled. So, I left with the equation, f = 10/2*180 = 10/360.

So, angular freq, f = ω/360 (Hertz) ..
where ω - Angular velocity in deg/sec

Am I thinking correctly?

6. Dec 19, 2011

### gsal

You are kind of correct..you just need to be more careful and keep things absolutely clear.

In your first posting, you never specified in which units ω was...typically, it is understood that it is in rad/s...what's more, you even included your starting equation as ω=2∏f...in this equation, ω is necessarily in rad/s!!! Then, suddenly, you replaced 2∏ with 360...what was I to think of this?

You see what I am coming from?

More often than not, it is best to keep things in radians or radians per second...you'll see.

7. Dec 19, 2011

### Staff: Mentor

Close enough.

Generally, ω is called the angular frequency and is measured in radians/second. f is just the frequency.

So, in standard units ω = 2πf. (Since one cycle = 2π radians.) But if you wanted the angular frequency in degrees/second instead, then ω = 360f. (Since one cycle = 360 degrees.)

I'm curious as to what context would give you an angular frequency in degrees/sec? I'd be very careful, since standard formulas for simple harmonic motion assume that ω is in radians/sec.

8. Dec 19, 2011

### sophiecentaur

This is particularly true when you start using Trig functions in Calculus. If you try to work in degrees, life becomes a nightmare.

It is worth while remembering that the three fingered Grigs of the planet Tryd will be dealing in exactly the same Radians that we deal in on Earth. However, their 'degrees' could be any fraction of a complete turn, depending on their particular culture - 1/360th, 1/350th, 1/297th or whatever.