A 10 g bullet traveling at 400 m/s strikes a 10
kg, 1.0-m-wide door at the edge opposite the hinge. The bullet embeds itself in
the door, causing the door to swing open.
What is the angular velocity of the door just
after impact?
For the 
system, the angular
momentum is conserved in the collision.
Solve: As the bullet hits the door, its velocity 
is perpendicular to 
Thus the initial
angular momentum about the rotation axis, with 
is
After the collision, with the bullet
in the door, the moment of inertia about the hinges is
Therefore, 
Using the angular
momentum conservation equation 
and thus 