16.90  (Fixed Axis Rotation, but of a composite body)

Comments/Hints:
1.  This is a composite body, consisting of a disk and a slender rod.  The mass center of the disk is at the pin at C, and the mass center of the slender rod is at the midpoint between A and B.  At the position shown, the assembly has an angular velocity of w = 10 rad/sec clockwise.
2.  Draw a free body diagram of the composite body.  It will show pin reactions Cx and Cy, the mg of disk C acting downward at pin C, and the mg of bar AB acting down at the midpoint of AB.
3.  Draw a kinetic diagram (KD) of the composite body.  There are two ways to do this:
(a)  Continue to treat the disk and the bar AB separately:  Draw both I_Ca and I_ABa couples, plus ma_n and ma_t terms at the mass center of AB.
(b)  Combine the disk and the rod into a single composite body with a single mass center and a single I.  (But this requires finding the mass center, etc.).  It's probably easier to do (a), that is, keep the bodies separate.
4.  I_C = 0.016 kg-m² (about the pin at C), and I_AB = 0.0018 kg-m²  (about the mass center of AB).  The ma_n term for the rod AB is mw²r = (1.5 kg)(102)(0.08 + 0.06) = 21.
5.  Write the equations of motion:  (a)  Sum forces in the horizontal (normal) direction = ma_n;  (b)  Sum forces in the vertical direction = ma_t; 
(c)  Sum moments about C = Sum of the kinetic moments about C = I_Ca + I_ABa + ma_t(0.14). 
6.  Solve for a = 43.6 rad/sec² CW, a_t = 0.14a = 6.11 m/s² downward;  and Cy = 54.6 N upward.