A 2.5-kg homogeneous disk of radius 80 mm rotates at the constant rate ω1 = 50 rad/s with...

A 2.5-kg homogeneous disk of radius 80 mm rotates at the constant rate ω1 = 50 rad/s with respect to arm ABC, which is welded to a shaft DCE. Knowing that at the instant shown, shaft DCE has an angular velocity ω2 = (12 rad/s)k and an angular acceleration α2 = (8 rad/s2)k, determine (a) the couple which must be applied to shaft DCE to produce that acceleration, (b) the corresponding dynamic reactions at D and E.

Fig. P18.104