Is there a simpler explanation for the equation \omega=\frac{2\pi}{T}=2\pi f?

[DB]

I saw this on Wikipedia
$$\omega=\frac{2\pi}{T}=2\pi f = v/r$$

What I don't understand is $$\omega= \\ \frac{2\pi}{T}=2\pi f$$
How can they be equivilant?

Thanks

 

[dextercioby]

THINK OF THE CIRCULAR MOVEMENT WITH CONSTANT ANGULAR VELOCITY...It will enlighten you.And a bit of trigonometry +geometry woudln't hurt at all...

Daniel.

 

[DB]

Let me clarify my question:
How can angular velocity be equivilant to 2pi divided by time in seconds and also equivilant to 2pi x hertz (in seconds obviously)? Isn't frequency dealing with circular motion revolutions per second?

 

[dextercioby]

Of course it is.That's what i suggested.
$$T=\frac{1}{\nu}$$

$$T=\frac{2\pi}{\omega}$$

$$\omega =2 \pi \nu$$

All of them are valid for circular motion...And completely equivalent...

WHAT IS ANGULAR VELOCITY...?

Daniel.

 

[DB]

ya, ya. I wasn't doubting they weren't equivilant. I just didnt understand why. I see it now though. Thanks man.

 

[cen2y]

Notice though that the so called "circular motion" which frequency must deal with would rather to be thought of metaphoricly. Circular as in a repeation of a certain entity and motion in the sense of things altering as the function of another variable. We may very well measure the frequency of people taking their dogs out on a walk or the frequency of wagons appearing on a merry go round wheel as the function of the distance along it's rim.