Meriam, Kraige & Bolton — Introduction to Three-Dimensional Dynamics of Rigid Bodies: Problem 7_90

7/90 An airplane has just cleared the runway with a take-off speed \(v\). Each of its freely spinning wheels has a mass \(m\), with a radius of gyration \(k\) about its axle. As seen from the front of the airplane, the wheel precesses at the angular rate \(\Omega\) as the landing strut is folded into the wing about its pivot \(O\). As a result of the gyroscopic action, the supporting member \(A\) exerts a torsional moment \(M\) on \(B\) to prevent the tubular member from rotating in the sleeve at \(B\). Determine \(M\) and identify whether it is in the sense of \(M_1\) or \(M_2\).