Conservation of Angular Momentum

[korbus]

Homework Statement

Indiana Jones standoff. Person A fires a 20g bullet at 500 m/s at Person B, who is holding a sword. The bullet sticks to the sword. The angular momentum of the sword is 2.225 kgm^2 / s. The moment of inertia about the center of mass of the sword is .7082 kgm^2. The sword is 1 meter long, and the center of mass is located at .5455 m.

Homework Equations

a. What was the initial angular momentum of the bullet as a function of distance from the center of mass of the sword?

The collision causes the sword to rotate and move but leaves the handle stationary.

b. Where did the sword take the bullet?

The Attempt at a Solution

Li = Lf
L = Iw

I(bullet)wi + I(sword)wi = Ifwf

I(bullet)wi + I(sword)wi = wf(I(bullet) + I(sword))

I(bullet)wi + I(sword)wi = wf(MR^2 + I(sword))

I(bullet)wi = wf(MR^2 + I(sword)) / I(sword)wi

... and I'm stuck there. Wouldn't I need to know what the final angular velocity of the system is in order to solve this problem?

Thanks for any suggestions.

 

[Andrew Mason]

The problem does not make it very clear where on the sword Person B is holding it. This is a rather important point.

The bullet imparts linear momentum to the sword and to Person B holding it. Prior to the collision, the bullet also has angular momentum with respect to the centre of mass of the sword. After the collision that angular momentum may or may not be conserved. It is not clear whether the sword is constrained so it is not possible to give an answer to this question based on the facts provided. It is also not clear from which end the distance to the centre of mass (.5455 m) is measured.

AM