The circular disk of 150-mm radius has a mass of 30 kg with centroidal radius of

Question

The circular disk of 150-mm radius has a mass of 30 kg with centroidal radius of gyration = 125 mm and has a concentric circular groove of 55-mm radius cut into it. A steady force T is applied at an angle ? to a cord wrapped around the groove as shown. If T = 28 N, ? = 0, ?s = 0.10, and ?k = 0.08, determine the angular acceleration ? of the disk, the acceleration a of its mass center G, and the friction force F which the surface exerts on the disk. The angular acceleration ? is positive if counterclockwise, negative if clockwise; the acceleration a is positive if to the right, negative if to the left; and the friction force F is positive if to the right, negative if to the left.

Explanation / Answer

MOI = M*k*k = 30*0.125*0.125 = 0.46875 kg.m2

Angular acceleration = Torque/I = 28*0.055/0.46875 = 3.285 rad/s2 (positive because moment of T is counterclockwise)

Static friction force = UsMg = 0.1*30*9.8 = 29.4 N

Kinetic friction force = UkMg = 23.52 N Since, static friction > T , the disk will roll without slip.

For this, angular acc. = a/r

a = 3.285*r = 0.49275 m/s2

F = 0 N, since, the body is in pure rolling, no friction force acts.

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