How Do You Calculate Angular Velocity for a Spinning Engine?

[Similis]

Hi

Can someone help me to demonstrate the 2 followed relations.

The dispositif is an engine who spin around himself

ώ = 2.(pi)/T

ώ is the angular velocity

thx and sorry for my bad english

 

[Mindscrape]

Is that supposed to be $$\dot \omega$$ as in $$\frac{d \omega}{dt}$$? I assume not.

I think that you are just trying to show that if
$$\omega = 2 \pi f$$
where $$\omega$$ is the angular frequency and f is the frequency, then an equivalent way of writing it is
$$\omega = \frac{2 \pi}{T}$$
using the relationship that $$f = 1/T$$