VERY IMPORTANT angular momentum

[fiziksfun]

In the following diagram:

http://i19.tinypic.com/7xaa148.jpg

A bullet of velocity 5 m/s hits an initially at rest rod. The mass of the bullet is 2kg.

The rod rotates around its axis in its top, I=(1/3)ML^2. It's mass of 3. It's distance is 4m. The rod finally stops moving after the collision at 90 degrees upward from the collision.

After the collision the bullet moves away at an angle of theta.

Kinetic energy is conserved. I used this to find both both vf and omega f of the bullet and rod.. but

HOW DO I FIND THETA?



any ideas?? PLEASE!?

 

[member 553083]

To find theta, you can use the conservation of angular momentum. The angular momentum of the system before the collision is zero, since the rod is initially at rest. The angular momentum of the system after the collision is the angular momentum of the bullet plus the angular momentum of the rod. Assuming the bullet and rod move in the same direction, the angular momentum of the system after the collision is: L = mv * r + (1/3)ML^2ω where m is the mass of the bullet, v is its velocity, r is the distance from the center of mass of the rod to the point of collision, M is the mass of the rod, and L is the length of the rod. The angle theta is then determined by the ratio of the angular momentum of the bullet and rod, since the total angular momentum must remain constant: theta = arctan(mv * r / (1/3)ML^2ω) You can then use the values for v, M, L, and ω calculated from the conservation of kinetic energy to solve for theta.