16.35 (Fixed Axis Rotation)
The weight and radius of the friction disk A are WA = 10 lb and rA
= 4.5 inch; the weight and radius of the friction disk B are WB
= 4 lb and rB = 3 inch. The disks are at rest when a 5 lb-in
couple moment M is applied to disk A. Assume no slipping between the
disks.
Determine: (a) The angular acceleration of each disk;
(b) The friction force that disk A exerts on disk B.
Comments/Hints:
1. Draw a separate free body diagram and kinetic diagram of each
disk. The FBD of disk A will have pin reactions, the couple M, the contact
friction force (from disk B), and (if you wish) a contact normal force.
The KD of disk A will have an IA·aA
term. The FBD of disk B will have pin reactions, the contact friction
force (from disk A, equal and opposite in direction), and (if you wish) a
contact normal force. The KD of disk B will have an IB·aB
term.
2. IA = 0.02184 slug-ft2, and IB =
0.003882 slug-ft2.
3. Write moment equations, one for disk A and another for disk B.
4. You need to relate aA vs. aB
using kinematics: You get aB
= 1.5aA.
5. Solve the two moment equations plus the kinematics equation to
get: aA = 13.63 rad/s2;
aB = 20.45 rad/s2 ; and F
= 0.3175 lb.