I'm having trouble with a simple impact/pendulum problem

[Strawberry]

Homework Statement

A bullet of mass 1 oz moving at a velocity 1000 ft/sec strikes and becomes embedded in a vertical pendulum rod of negligible mass 10 inches from the top of the rod where the rod is fixed, but allowed to move in the direction of the bullet. The rod is 20 inches in total length and a mass of 3 kg, which may be considered a particle at the end of the 20 inch rod, is attached.

(Basically a bullet strikes the middle of a pendulum that has all its weight concentrated at the bottom)

Find the angular velocity directly after impact, and explain why linear momentum is not conserved.

Homework Equations

I don't understand how to approach this problem conceptually. I do not believe that energy is conserved during this impact, and it states that linear momentum is not conserved in this system. Is angular momentum conserved then? Can I even use the (mass of the bullet) x (radius from the origin where it strikes the pendulum) x (velocity of the bullet) as a linear momentum? It should be a moment (r x F) instead, right? I don't know where to go with this.

The Attempt at a Solution

I attempted to set the initial angular momentum (the velocity of the bullet times the distance away from the fulcrum of the pendulum where it hit times the mass of the bullet) equal to the final angular momentum (the combined mass times the center of gravity? times the unknown velocity), but I do not think that is correct. I'm not really sure why linear momentum is conserved during the instantaneous impact either, unless it's because the pendulum is restricted at the top?

 

[Doc Al]

I do not believe that energy is conserved during this impact,

Right. It's a perfectly inelastic collision.

and it states that linear momentum is not conserved in this system.

Right.

Is angular momentum conserved then?

Yes!

Can I even use the (mass of the bullet) x (radius from the origin where it strikes the pendulum) x (velocity of the bullet) as a linear momentum?

You mean angular momentum, but yes.

It should be a moment (r x F) instead, right?

No, torque would equal the rate of change of angular momentum. You don't have information about the forces exerted anyway.

I attempted to set the initial angular momentum (the velocity of the bullet times the distance away from the fulcrum of the pendulum where it hit times the mass of the bullet) equal to the final angular momentum

Good.

(the combined mass times the center of gravity? times the unknown velocity), but I do not think that is correct.

It's not correct. Hint: Find the total moment of inertia of the system about its axis of rotation.

I'm not really sure why linear momentum is conserved during the instantaneous impact either, unless it's because the pendulum is restricted at the top?

Do you mean is *not* conserved? Yes, the pivot doesn't move and thus exerts an external force (but not torque) on the system.