If a ball hits a rod at rest at any position along the rod, the rod will be moving with the same linear velocity in each case. However, if the ball hits the rod away from its center of mass, the rod will also rotate.
How does this not violate the conservation of energy? The incoming ball has the same mass and velocity in each case and thus the same energy is inputted to the system, and the rod will have the same mass and linear velocity in each case, plus excess rotational energy. How can simply choosing where the ball hits the rod add energy to the system? My best guess is that hitting the rod off-center somehow "drains" more energy from the ball and slows it down more after collision, but I dont quite see why this would occur mechanistically.