Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 53_M

In Fig. 11.28 (an over head view), a uniform thin rod of length 0.500 m and mass 4.00 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 3.00 g bullet traveling in the rotation plane is fired into one end of the rod. In the view from above, the bullet’s path makes angle \(\theta = 60.0^\circ\) with the rod (Fig. 11.28). If the bullet lodges in the rod and the angular velocity of the rod is 10 rad/s immediately after the collision, what is the bullet’s speed just before impact?