Bullet hits cylinder angular speed

[AltruistKnight]

Angular Velocity After Bullet Hits Cylinder

Homework Statement

A 11.0g bullet is fired at 378.1m/s into a solid disk of mass 19.1kg and a radius 0.250m. The disk is initially at rest and is mounted on fixed vertical axis that runs through it's center of mass. The line of motion of the bullet is perpendicular to the axis and at a distance 5.00cm from the center. Find the angular velocity of the system after the bullet strikes and adheres to the surface of the disk.

Homework Equations

Linear Momentum (P)=m*v
Angular Momentum (L) from Linear Momentum(P)=m*v*r
Angular Momentum (L)=Moment of Interia*Angular Speed
Torque=F*r
Angular Speed ("Omega")=Change in Angle/t
Parallel Axis Theorem:Icm=Icm@Point+MR^2

The Attempt at a Solution

Prior to collision, all the inertia is in the positive x-direction according to my coordinate system, and belongs solely to the bullet. This would be linear momentum. However, after the collision, the bullet becomes embedded in the cylinder, which begins to turn in order to conserve the bullet's momentum.

Thus:

mv(Bullet)=I(Bullet+Cylinder)Omega

But does radius only come into play with calculating the system's moment of inertia post-collision? (And would I find the moment of inertia of the embedded bullet by assuming its embedded 5cm above the center, and then using the parallel axis theorem? Would I then just find the moment of inertia of the cylinder via a solid cylinder equation, add the two, and solve the momentum equation I showed above?)

If anyone could help me out ASAP with this that'd be great; my assignments are computerized and are only telling me I'm wrong rather than actually helping me realize whether it's the math or just my conceptual thought >_<

 

[TSny]

Hello, AltruistKnight.

mv(Bullet)=I(Bullet+Cylinder)Omega

Linear momentum and angular momentum have different dimensions (units). So, they can't be set equal to one another. Can you find the angular momentum of the bullet about the axis of rotation of the disk just before the bullet strikes the disk? (Treat the bullet as a particle and review the definition of angular momentum of a particle.)

But does radius only come into play with calculating the system's moment of inertia post-collision? (And would I find the moment of inertia of the embedded bullet by assuming its embedded 5cm above the center, and then using the parallel axis theorem? Would I then just find the moment of inertia of the cylinder via a solid cylinder equation, add the two, and solve the momentum equation I showed above?)

The bullet can be treated as a point particle that rotates with the disk after the collision. You should have studied how to find the moment of inertia of a single particle that moves in a circle. Then, as you said, you can add this to the moment of inertia of the solid cylinder.