Discussion and hints:
Recall the following four-step plan outline in the lecture book and discussed in lecture:
Step 1: FBDs
Draw individual free body diagrams for the bar and the particle. These FBDs will include the equal-and-opposite impact force pair on the bar and on the particle.
Step 2: Kinetics (impulse/momentum)
- Write down the impulse/momentum equation for the particle in terms of the impulse of the impact force on the particle.
- Write down the angular impulse/momentum equation for the bar in terms of the angular impulse of the impact force on the bar.
- Combine the above two equations.
Step 3: Kinematics
Note that here the particle sticks to the end of the bar. Therefore, the particle has the same post-impact velocity as the upper end of the bar. You will need to use the rigid body velocity equation to relate the velocities of the center of mass of the bar and the end of the bar through the angular velocity of the bar.
Step 4: Solve
Solve your equations above for the velocity of the center of mass of the bar.
Any questions?