Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_43

6/43 An air table is used to study the elastic motion of flexible spacecraft models. Pressurized air escaping from numerous small holes in the horizontal surface provides a supporting air cushion which largely eliminates friction. The model shown consists of a cylindrical hub of radius \(r\) and four appendages of length \(l\) and small thickness \(t\). The hub and the four appendages all have the same depth \(d\) and are constructed of the same material of density \(\rho\). Assume that the spacecraft is rigid and determine the moment \(M\) which must be applied to the hub to spin the model from rest to an angular velocity \(\omega\) in a time period of \(\tau\) seconds. (Note that for a spacecraft with highly flexible appendages, the moment must be judiciously applied to the rigid hub to avoid undesirable large elastic deflections of the appendages.)