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## 07 Jan A 2.5 ktg homogenous disk of radius 80 mm can rota

A 2.5 ktg homogenous disk of radius 80 mm can rotate with respect to arm ABC, which is welded to a shaft DCE supported by bearings at D and E. Both the arm and the shaft are of negligible mass. At time t = 0 a couple M0 = (0.5 N . m)k is applied to shaft DCE. Knowing that at t = 0 the angular velocity of the disk is ω1 = (60 rad/s)j and that friction in the bearing at A causes the magnitude of V1 to decrease at the rate of 15 rad/s2 , determine the dynamic reactions exerted on the shaft by the bearings at D and E at any time t. Resolve these reactions into components directed along x and y axes rotating with the shaft. Use computational software (a) to calculate the components of the reactions from t = 0 to t = 4 s (b) to determine the times t1 and t2 at which the x and y components of the reaction at E are respectively equal to zero.

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