Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_137

6/137 The 165-lb flywheel has a radius of gyration about its shaft axis of $k = 20 \text{ in.}$ and is subjected to the torque $M = 8(1 - e^{-t}) \text{ lb-ft}$, where $t$ is in seconds. If the flywheel is at rest at time $t = 0$, determine its angular velocity $\omega$ at $t = 3 \text{ sec}$.