Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_66

6/66 The fairing which covers the spacecraft package in the nose of the booster rocket is jettisoned when the rocket is in space where gravitational attraction is negligible. A mechanical actuator moves the two halves slowly from the closed position I to position II at which point the fairings are released to rotate freely about their hinges at $O$ under the influence of the constant acceleration $a$ of the rocket. When position III is reached, the hinge at $O$ is released and the fairings drift away from the rocket. Determine the angular velocity $\omega$ of the fairing at the 90° position. The mass of each fairing is $m$ with center of mass at $G$ and radius of gyration $k_O$ about $O$.