Answer to Question #277566 in Physics for Sks

Question

A door with width 1.2 m and mass M = 10 kg is hinged on one side so that it can rotate

freely. A bullet is fired into the center of the door. The bullet has mass 25 g and a speed of

300 m/s. What is the angular velocity of the door with respect to the hinge just after the

bullets embeds itself in the door?

Answer 1

By energy conservation:

$$\frac12 mv^2=\frac12I\omega^2,\\\space\\ \frac12 mv^2=\frac12·\frac13ML^2·\omega^2,\\\space\\ \omega=\frac vL\sqrt{\frac{m}{M}}=12.5\text{ rad/s}.$$