Spin Angular Momentum - Bullet hitting bottom of a thin rod?

[mintsnapple]

Homework Statement

Homework Equations

The Attempt at a Solution

Angular momentum is the only parameter conserved. This is because there are no external torques acting on the system. Energy is not conserved because the collision is inelastic. Finally, linear momentum is not conserved because there is an external force acting on the rod's center of mass that prevents the system from moving forward after the collision.

Now, for part d, I am not so sure what to do. Should I equate the angular momentum of the system before the bullet hits with the final angular momentum of the system, solve for angular velocity, and turn that into linear velocity? Though I have no idea how g would come into play..

 

[BvU]

Your plan to get going is good. After the embedding of the bullet, the thing is just a kind of pendulum (a variation on the ballistic pendulum).

If you fill in the relevant equations under 2, you automatically get to see the role of g.