So, we are learning about simultaneous rotational and translational motion. I understand that they can be dealt with independently -- for example, if 2 identical rods have a force applied to them at different points, their rotational motion will differ but they will both have the same center-of-mass acceleration. But I am having a really hard time understanding WHY this is. It seems like if a force was applied to the end of the rod, some of the energy given would go towards spinning the rod, and it would move less (translationally) than if a force was applied at the center of one side of the rod. Can anyone clarify why this is not the case? Relatedly I am having trouble understanding how 2 identical objects given the same force can end up with different total kinetic energies, due to one of them having a rotational component of KE. It just doesn't make sense to me intuitively.