a uniform thin rod of length 0.50 m and mass 4.0 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 3.0 g bullet traveling in the horizontal palne of the rod is fired into one end of the rod. The direction of the bullet's velocity makes an angle of 60 degrees with the rod. If the bullet lodges in the rod and the angular velocity of the rod is 10 rad/s immediately after the collision,
a) For the system of the rod and bullet, is linear momentum, angular momentum, or mechanical energy conserved in this collision?
b) what is the magnitude of the bullet's velocity just before the impact?
c) Determine the fractional loss in kinetic energy due to the collision.