# Angular frequency=2*pi*frequency

1. Jun 30, 2013

### pyroknife

This is not a homework problem, but something that came to my attention.

I attached a pic.
The thin horizontal line in the pic represents the axis of rotation of pin. So the 1st one is rotation from +30 to -30 degrees and the second from 10 to -10 degrees.
Let's assume both are rotating at 3Hz.

So my question is that the equation ω=2*∏*f doesn't hold for this case right?
If both are rotating at 3Hz, then the drawing on the left must be rotating at a larger angular speed because the amplitude is bigger.

Is ω=2*∏*f only for something that experiences a cycle of 360 degrees?

For the figure on the left, one cycle is 60 degrees, so 3 cycles is 180 degrees. So that means the angular speed is 180 degrees/s.

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2. Jun 30, 2013

### dreamLord

No, they have the same angular frequency. Perhaps you are thinking that both the rotations take the same amount of time - which is not true. The pin could complete a whole circle of 360 degrees at the same angular frequency - the angle through which it turns has nothing to do with how often it retraces it's path . The left pin has covered 60 degrees, which is 1/6th of a full cycle - hence it takes half a second. The right pin has covered 20 degrees, which is 1/18th of a full cycle - hence it takes 1/6th of a second.

I'm not sure I understood your question properly though, so let someone smarter answer.

Last edited: Jun 30, 2013
3. Jun 30, 2013

### pyroknife

The problem is really confusing me.
I thought angular frequency was how many radians/degrees it travels per second. If both have the same frequency (cycles/second) and the angular amplitude for the one on the left is bigger, wouldn't that one have to rotate at a faster speed to achieve the same cycles per second?

4. Jun 30, 2013

### dreamLord

Yes, angular frequency is how many degrees the particle travels per second. So with a frequency of 3 Hz, you get an angular frequency of 2 * pi * 3 = 18.84 radians per second.

Now let's say a particle traverses one radian (180 degrees) - that means it takes it 18.84 seconds. If another particle traverses 2 radians (360 degrees), then it would take it 18.84 * 2 = 37.68 seconds. Different times taken though they had the same angular frequency.

5. Jul 1, 2013

### Clandry

I am pretty sure that the ω=2*∏*f only applies to continuous rotations. In your setup, the angular displacement is discontinuous at the max and mins. The setups are not rotating at the same speed=>they have diff. angular frequencies.

6. Jul 1, 2013

### dreamLord

I don't get it - how are they discontinuous? Hasn't the OP shown us parts of a rotation - one which covered 60 degrees, and the other 20 degrees?

7. Jul 1, 2013

### Clandry

He showed us the "whole" rotation, not parts. Refer to the OP where it mentioned "axis of rotation." It's oscillating between the + and - angles.

8. Jul 1, 2013

### barryj

I tend to sense some confusion here. Is the rotation in a plane, or is the rotation about the center line and is in fact rotating on the surface of a cone. How you picture the problem makes a difference.

9. Jul 1, 2013

### pyroknife

Basically, the picture I attached is a top view of a thin panel. So if you look from the top view it's rotating from a positive angle to a negative angle. Does that make sense?