Adoor 1.00m wide, of mass 15kg can rotate freely about a vertical axis through its hinges. a bullet with a mass of 10 g and a speed of 400 m/s strikes the center of the door, in a direction perpendicular to the plane of the door, and embeds itself there. find the door's angular speed. is kinetic energy conserved? physics final

This question contains collision of rotational objects, so we should use angular momentum.

or

By conversation of angular momentum;

since the bullet hits the door in a direction perpendicular to the plane of the door.

, the distance from the center of the door to the hinges.

After the collision the bullet embeds itself to the door. Now the door and the bullet is a combined object with mass 15,01 kg.

where is the width of the door, and the bullet can be considered as a point particle.

Explanation:

The calculation of moment of inertia of a rectangular door rotating around its hinges is a bit long. But the answer is in every standard textbook. It is safe to use it without deriving it ourselves.

i think it's 35 meters