In one of his lectures, Walter Lewin gives the example of a rod which is hit with an impulse on its edge. It starts rotating with angular velocity w, and its center of mass moves with velocity v. Assuming ideal conditions, he then continues to explain that where the object is hit does not matter, the center of mass will always move with velocity v given impulse I. In other words, if the rod was hit right at its center of mass with impulse I, it would still move with velocity v without rotating. I thought that was very unintuitive if we think about energy considerations. My gut instinct told me that the one hit at the center would move with a higher velocity.
If it is truly the case that the center of mass will always move with velocity v, it would seem to me that the one hit at the edge has more energy since it has both rotational and translational kinetic energy (where the latter is equal to the translational kinetic energy of case when it is hit right at its center of mass, since they have the same velocity v). This is despite the fact that the one hit at the edge was acted upon by the same impulse i.e same force as the one hit at the center which only has translational kinetic energy. So how do we reconcile this?
EDIT: Check out video Bullet Block Experiment Result.