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A bullet with mass m and a velocity of v is shot perpendicular to the edge of a uniform rod with length L and mass 4m which is free to move and rotate on a frictionless horizontal surface. The bullet is lodged into the rod and move together after the collision. a) Calculate the linear velocity of the center of mass of the system (rod-bullet) after the collision. b) Find the position (on the rod) of center of mass of the system (rod-bullet) after the collision. c) Find the moment of inertia of the system around the axis through the center of mass. d) Calculate the angular velocity ω of the system after the collision. (The moment of inertia of a uniform rod about its center of mass is mL2/12.)

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