Dimensional formula of angular velocity

Angular velocity
[T−1]
Written in full: [M⁰ L⁰ T⁻¹ A⁰ K⁰]

How to derive it

Angular velocity = Angle ÷ Time (angle has no dimensions)

Put in the dimensions of each part: [M⁰L⁰T⁰] ÷ [T] = [T⁻¹].

mass (M)
0
length (L)
0
time (T)
-1
current (A)
0
temperature (K)
0

SI unit

The SI unit of angular velocity is rad/s.

Same dimensions as angular velocity

These quantities have exactly the same dimensions, a favourite trick in JEE and NEET "which pair has the same dimensions" questions:

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More from Rotational motion

QuantityFormula
Angular acceleration[T−2]
Torque[M L2 T−2]
Moment of inertia[M L2]
Angular momentum[M L2 T−1]