The 30-kg spool of outer radius ro = 400 mm has a centroid radius of gyration k = 300 mm and a central shaft of radius ri = 150 mm. The spool is at rest on the inclined path of θ = 30^o when a tension T = 300 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 angular acceleration of the spool for:..

A. There is enough friction that spools roles without slip.

B. The spool rolls with slip and coefficient of friction is 0.1

C. We do not know if the spool rolls with slip or not, but the coefficient of friction is 0.2.

 

J