Discussion and hints:
Recall the following four-step plan outline in the lecture book and discussed in lecture:
Step 1: FBDs
Draw a single free body diagram for the system made up of the disk, bar and block, combined.
Step 2: Kinetics (work/energy)
- Write down the kinetic expressions for the three bodies in the system, individually, and then add those together to find the total KE for the system of your FBD.
- Do the same for the potential energies: write down the PEs for each body individually and add together.
- Also, based on your FBD above, which, if any force or couple, does nonconservative work on the system in your FBD? Determine work for such a force/couple.
Step 3: Kinematics
Since the bar is welded to the disk, the angular velocities of the bar and disk are the same. The no-slip condition at the point of contact of the disk and block enforces a constraint between the rotation rate of the disk and the translational speed of the block. What is that constraint?
Step 4: Solve
Solve your equations above for the angular velocity of the disk.