17.31 (Rigid Body Work Energy Equation) (Sorry for the tilt!)
Comments/Hints:
1. Disk A rolls down the right hand rope; thus disk A stores kinetic
energy in both translation (T = 1/2·mA·vA2 )
and rotation (T = 1/2·IA·wA2
).
2. Disk B rotates about a fixed pin, so it stores energy in rotation only
((T = 1/2·IB·wB2
).
3. The only work done is the mass center of disk A falling 3 ft.
4. Use the work-energy equation: ST1 + SU1-2
= ST2
5. You need kinematics relationships: wB
= 2wA, and vA = 5/12·wA.
6. Answers: wA = 17.83
rad/sec, vA = 7.43 fps, and wB
= 35.66 rad/sec.