> [!summary] Angular speed describes how fast an object is rotating around a circle > **Key Equations:** > Angular speed: $\omega = \frac{d\theta}{dt}$ > If the angular speed is constant: $\omega= \frac{2\pi r}{T}$ >[!info]+ Read Time **⏱ 1 min** # Definition Angular speed is a [[Scalar & Vectors|scalar quantity]] and tells you how fast you are rotating around a circle. Mathematically, this is the [[Instantaneous|instantaneous change]] of [[Angular Displacement|angular displacement]] $ \omega = \frac{d\theta}{dt} $ > [!note] If angular speed is always constant If angular speed is always constant around a circle, then the angular speed can also be described as the time it takes to loop around a circle with circumference $2\pi r$ or > > $ \omega = \frac{2\pi r}{T} > $ --- > 📚 Like this note? [Star the GitHub repo](https://github.com/rajeevphysics/Obsidian-MathMatter) to support the project and help others discover it! ---