rad/s and s^-1 are the same unit. Radians are dimensionless.

Also in this case $\omega$ is an angular frequency, not an angular velocity. So you can use either $\omega$ or $f$. It doesn't matter. They are essentially the same thing. $\omega=2\pi f$

$\rm{rad/s}$ and $\rm{s^{-1}}$ are the same unit. Radians are dimensionless.

Also in this case $\omega$ is an angular frequency, not an angular velocity. So you can use either $\omega$ or $f$. It doesn't matter. They are essentially the same thing. $\omega=2\pi f$