Angular velocity ($\omega$) is defined as the time rate of change of angular displacement ($\omega = \frac{d\theta}{dt}$).

1. Angular Displacement ($\theta$): It is defined as the ratio of arc length to radius ($\theta = s/r$). Being a ratio of two lengths, it is a dimensionless quantity with dimensions $[M^0L^0T^0]$.
2. Time ($t$): The dimension of time is $[T]$.
3. Dimensional Formula: Substituting these into the definition: $[\omega] = \frac{[\theta]}{[t]} = \frac{[M^0L^0T^0]}{[T]} = [M^0L^0T^{-1}]$