Question #42249

A gyroscope consists of a uniform solid disk of mass $M = 2 \text{ kg}$ and radius $R = 0.1 \text{ m}$ mounted on a massless axle. The axle is attached to a frictionless pivot on the vertical axis of a rotating platform. The distance from the pivot to the center of mass of the disk is $L = 0.2 \text{ m}$. The platform rotates at a constant angular velocity $\Omega = 10 \text{ rad/s}$ about the vertical axis. The gyroscope axle is observed to maintain a steady angle $\theta = 60^\circ$ with the upward vertical, precessing together with the platform. Calculate the required spin angular velocity $\omega$ of the disk about its axle. (Take $g = 10 \text{ m/s}^2$)