calculating angular velocity

I am confused and having trouble calculating the corresponding frequency for the phasor 628 rad/s.

Given the formula w= 2*pi*f where pi = 3.14.. and f = frequency in Hertz, how would I be able to calculate the answer?

Help is much appreciated. Thanks!

 

Conversions in angular measure are based on the full circle.

One full circle corresponds to one cycle so.

One full circle per second equals one Hertz.

A full circle has 360 degrees.

A full circle has 2π (pi) radians.

So 1 full circle per second is equal to 2π rads per second. (your formula)

So 1/2π full circles is equal to 1 rad per second

So 628/2π full circles per second is equal to 628 rads per second

or

628/2π Hz = 628 rads/s

 

w= 2*pi*f

if you solve for f you get:

f=w/(2*pi)=628/(6.28)=100 Hz

 

That cleared up the confusion I had. Thanks for the replies!