Problem

The disk D, which has weight W, mass center G coinciding with the disk’s geometric center,...

The disk D, which has weight W, mass center G coinciding with the disk’s geometric center, and radius of gyration kG, is at rest on an incline when the constant moment M is applied to it. The disk is attached at its center to a wall by a linear elastic spring of constant k. The spring is unstretched when the system is at rest. Assuming that the disk rolls without slipping and that it has not yet come to a stop, determine the angular velocity of the disk after its center G has moved a distance d down the incline. After doing so, using k = 5 lb/ft, R = 1.5 ft, W = 10 lb, and θ = 30°, determine the value of the moment M for the disk to stop after rolling ds = 5 ft down the incline.