Angular Velocity

Summary

Angular velocity states how fast an object is rotating in a direction

Key Equations:

Angular velocity:
$\vec{ω} = \frac{d θ}{d t} = \frac{Δ s}{Δ t \cdot r} = \frac{v}{r}$

Tangential angular velocity:
$\vec{ω_{t}} = ω r$

Read Time

⏱ 1 min

Definition

Angular velocity is a vector quantity that tells you how fast an object is rotating around a circle and the direction it is rotating. Mathematically, it is the instantaneous change of angular displacement

\vec{ω} = \frac{d θ}{d t} = \frac{Δ s}{Δ t \cdot r} = \frac{v}{r}

Tangential component

Since angular velocity a vector on a curve, it will have two components. One being its tangential component defined as the angular velocity a distance away from rotation.

$\vec{ω_{t}} = ω r$

Resources

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