Good morning!
We have that:
60 rpm = 60 rot / min = 60 rot / 60 s = 1 rot/s
However, 1 rot/s = 1 Hz
So, we have a frequency of f =1 Hz.
We know that:
[tex]\mathsf{\omega = 2\pi f}\\ \\ \mathsf{\omega = 2\pi 1}\\ \\ \boxed{\mathsf{\omega = 2\pi\ rad/s}}[/tex]