A uniform rod of mass M and length L is initially motionless. A piece of putty of the same mass travels at speed v0 perpendicular to the rod strikes the rod at its very end, as shown in the figure, and sticks to it. At the instant of the collision, the center of mass of the system is located at the position marked with an x in the figure. a) Find the velocity of the center of mass of the system after the collision. b) Use conservation of angular momentum with respect to the position of the center of mass at the moment of collision to find the angular speed of the system after the collision. c) Imagine the rod was pivoted on its top end. What would be the angular speed of the system after the collision?

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