Period versus (inverse) rotation_speed?

[Capiert]

Period versus 1/(vc),

frequency versus vc ?

 

I find it very confusing

 that rotation_speed vc=2*Pi*r/t

 looks (very similar, &) proportional

 to frequency f (cycles per second;

 or (1) cycle (e.g. circle) per time

 (in units of seconds,

 or less than a second));

 & inverted_rotation_speed 1/(vc)=t/(2*Pi*r)

 (the time "per" cycle_or_circle_(circumference))

 looks proportional to Period T=1/f

 which is inverted_frequency!

(Thus units are suppose to be inverted.)

 

So (confusing) that I must start

 with what we know.

In fact I am so confused,

 that I know nothing

 except the rotation_speed vc=2*Pi*r/t

 (which is obvious),

 & the frequency f=1/T inverse_period relation (definition).

The rest seems (to me) like non_sense!

Thus I can derive everything (I need)

 from what we know:

 

The circumferential_speed

 vc=cir(cle)/t(ime)

 vc=2*Pi*r/t. ~f.

That looks like

 

 cycles (=circles) "per" second

 

 =[cps]=[c/s].

 (Units in square brackets.)

I.e. That looks (very much) like frequency!

(Although you guys are only interested

 in the inverse(=1_divided_by)_time 1/t

 for the "number" value of f (without units,

 =excluding units [c/s]).

 

We also know the "inverse" circumferential_speed

 1/(vc)=t(ime)/cir(cle)

 1/(vc)=t/(2*Pi*r). ~T.

That looks like

 the time_(in seconds)_"per"_cycle(=circle)

 =[spc]=[s/c].

I.e. That looks (very much) like the Period!

(Although you guys are only interested

 in time t

 for the "number" value of T (without units,

 =excluding units [s/c]),

 because you have defined

 frequency f=1/T as inverse_period.

 

So the

 time ("for" a cycle) is

 t=(2*Pi*r)/(vc)

 time=(circle (or cycle)) "per" rotation_speed).

That is the (number) value for what you guys call period (T).

Your units are seconds (because all circles cancel).

 

It's inverse

1/t=vc/(2*Pi*r)

 inverted_time=rotation_speed "per" (1) circle (or cycle),

 gives the number (value)

 for what you (guys & gals) call frequency (f).

In other words, stripped of the cycle(s).

 

You now have units [Hz] Herz (=hurts! Ouch!)

 

Edited December 31, 2018 by Capiert

[Endy0816]

Yeah we typically don't, but you can use frequency anywhere you see time and it'll still  be valid.

ie.

vc = Area/t = Area×frequency

vc = Circumference/t = Circumference×frequency

Edited December 31, 2018 by Strange
Corrected

[Strange]

10 hours ago, Capiert said:

I find it very confusing

Because you insist on using this affected writing style, it is almost impossible to see what you are confused about. 

You seem to be happy that period (the time between one cycle and the next) is 1/f.

And you seem to understand that rotational speed is the length of the circumference dividing by the time to perform one rotation.

There doesn't seem to be anything else to say, or be confused about.

Maybe if you could write a single sentence, like a normal adult, explaining the problem it might be possible to understand you. 

But if you continue to write incoherent nonsense, filled with random punctuation, then I doubt anyone can help. 

[Endy0816]

Ugh correction, Circumference not Area.

 

This video of a sinewave being traced out from a circle's rotation might make the connection clearer.

 

[Strange]

4 minutes ago, Endy0816 said:

Ugh correction, Circumference not Area.

That was a good point, well made apart from that error, so I have corrected it for you (assuming it was too late for you to do it).

[Endy0816]

1 hour ago, Strange said:

That was a good point, well made apart from that error, so I have corrected it for you (assuming it was too late for you to do it).

Oh thanks! Appreciate that. Hate when I miss that cut off lol

 

Keep forgetting there are Apps for everything now. A stroboscope makes frequency far more relatable.

You can visually freeze things by matching the two frequencies.