The dimensional formula of angular velocity $\left(\omega=\cfrac{v}{r}\right)$ is

The angular velocity of a body is given by:

$\omega=\cfrac{V}{r}$

The dimension of $V=[LT^{-1}]$

The dimension of $r=[L]$

$\omega=\cfrac{LT^{-1}}{L}=T^{-1}$

$\omega=M^0L^0T^{-1}$

Another way to show this is,

angular velocity=revolutions per second

As ‘revolutions’ is dimensionless, the dimension of angular velocity must be [T^-1]