Meriam, Kraige & Bolton — Plane Kinetics of Rigid Bodies: Problem 6_64

6/64 The 30-kg spool of outer radius \(r_o = 450 \text{ mm}\) has a centroidal radius of gyration \(\bar{k} = 275 \text{ mm}\) and a central shaft of radius \(r_i = 200 \text{ mm}\). The spool is at rest on the incline when a tension \(T = 300 \text{ N}\) is applied to the end of a cable which is wrapped securely around the central shaft as shown. Determine the acceleration of the spool center \(G\) and the magnitude and direction of the friction force acting at the interface of the spool and incline. The friction coefficients there are \(\mu_s = 0.45\) and \(\mu_k = 0.30\). The tension \(T\) is applied parallel to the incline and the angle \(\theta = 20^\circ\).