A uniform thin rod of length 0.500 m and mass 5 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 5.00 g bullet traveling in the rotation plane is fired into one end of the rod. As viewed from above, the bullet's path makes angle ϴ = 60° 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, what is the bullet's speed just before impact? given=1/12 ML²

A uniform rod of length L = 2.0 m and mass M = 5.0 kg on a frictionless tabletop freely rotates counterclockwise about a central axle at an angular speed wp = 3.0 rad/s. A small mass m = 0.53 kg slides along the table top and sticks to the rod a distance 0.67 m away from one end of the rod. Just before sticking, the direction of the velocity of the small mass is perpendicular to the line of the rod (see figure). After sticking, the mass and the rod come to a complete stop. Given that the rotational inertia of a rod about an axis through its center is / =ML2/12, the incoming speed of the small mass is (Enter your answer in units of m/s. Only enter the number using 2 significant figures.)

A solid, horizontal cylinder of mass 15.0 kg and radius 1.00 m rotates with an angular speed of 6.00 rad/s about a fixed vertical axis through its center. A 0.250-kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system.

A uniform solid disk of mass m = 2.95 kg and radius r= 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 5.98 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. kg · m²/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim? kg - m²/s