This example demonstrates how a particle moving in a straight line can carry angular momentum. Specifically, we will see that the straight$-$line motion of a particle can, in fact, induce rotational motion after an impact. A uniform door $1\mathrm{.}0$ m wide with a mass of $15$ kg is hinged at one side so that it can rotate without friction about a vertical axis. The door is unlatched. A police detective fires a bullet with a mass of $10$ g and a speed of $400$ m$/$s into the exact center of the door in a direction perpendicular to the plane of the door. Find the angular velocity of the door just after the bullet is embedded in it$.$ Is kinetic energy conserved?

Suppose the bullet goes through the door and emerges with a speed of $65$ m$/$s$.$ Find the final angular velocity of the door just after the bullet goes through it$.$