The dimension of angular velocity is

Correct Option: [M⁰L⁰T⁻¹]

To find the dimension of angular velocity, we can break it down using its definition and formula.

Step 1: Understand Angular Velocity
Angular velocity (represented by the Greek letter omega, $\omega$) is defined as the rate of change of angular displacement ($\theta$) with respect to time ($t$). The formula is given by:
$\omega =\frac{d\theta }{dt}$

Step 2: Determine the Dimensions of the Component Quantities
1. Angular displacement ($\theta$): Angular displacement is measured in radians. By definition, angle is the ratio of arc length to radius:
$\theta =\frac{\text{Arc Length}}{\text{Radius}}$
Since both arc length and radius are measured in units of length, their dimensions cancel out:
$\left[\theta \right]=\frac{\left[L\right]}{\left[L\right]}=\left[M^0{L}^0{T}^0\right]$
Thus, angular displacement is a dimensionless quantity.
2. Time ($t$): The dimension of time is represented as $\left[T\right]$.

Step 3: Calculate the Dimension of Angular Velocity
Substituting these dimensions into the formula for angular velocity:
$\left[\omega \right]=\frac{\left[M^0{L}^0{T}^0\right]}{\left[T\right]}=\left[M^0{L}^0{T}^{-1}\right]$
Therefore, the dimensional formula of angular velocity is [M⁰L⁰T⁻¹].