* Angular velocity (ω) is defined as the rate of change of angular displacement (θ) with respect to time (t).
* Angular displacement (θ) is dimensionless (it's the ratio of arc length to radius).
* Time (t) has the dimension of T.
Therefore, the dimension of angular velocity is:
ω = θ/t = [dimensionless]/T = T⁻¹
In simpler terms:
* Angular velocity is measured in radians per second (rad/s).
* Radians are dimensionless, leaving only the dimension of time in the denominator.
* This means that angular velocity has the dimension of inverse time (T⁻¹).
