> [!summary] Rotational work measures the energy transferred from the rotational force on an object > **Key Equations:** > Rotational work: $W =\int_{a}^b \tau \cdot d\theta$ >[!info]+ Read Time **⏱ 1 min** # Rotating Work Rotational work measures the [[Energy|energy]] transferred when a force moves an object rotationally. An object will only rotate when a [[Torque|torque]] is applied to it. So mathematically, rotational work is the integral of [[Torque|torque]] [[Dots Product & Angles|dotted]] with [[Angular Displacement|angular displacement]]. $ W= \int_{a}^b \tau \cdot d\theta $ > [!note] There is a [[Dots Product & Angles|dot product]] between [[Torque|torque]] and [[Angular Displacement|angular displacement]] because only the [[Tangential & Perpendicular|perpendicular]] force contributes to rotational motion.