> [!summary] Angular velocity states how fast an object is rotating in a direction > **Key Equations:** > Angular velocity: $\vec{\omega} = \frac{d\theta}{dt} =\frac{\Delta s}{\Delta t\cdot r} = \frac{v}{r}$ > Tangential angular velocity: $\vec{\omega_{t}}=\omega r$ >[!info]+ Read Time **⏱ 1 min** # Definition Angular velocity is a [[Scalar & Vectors|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|instantaneous change]] of [[Angular Displacement|angular displacement]] $ \vec{\omega} = \frac{d\theta}{dt} =\frac{\Delta s}{\Delta t\cdot r} = \frac{v}{r} $ > [!note] Tangential component Since angular velocity a vector on a curve, it will have two components. One being its [[Tangential & Perpendicular|tangential component]] defined as the angular velocity a distance away from rotation. > $\vec{\omega_{t}}=\omega r$ # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/1SWPlmsJGoE?si=G43Mz6XHo_OPOL-P" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe> --- > 📂 Want to see more structured notes like these? > Help grow the project by [starring Math & Matter on GitHub](https://github.com/rajeevphysics/Obsidian-MathMatter). ---