Conceptual question - rotational+translational motion

[rbigongi]

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.

 

[tiny-tim]

welcome to pf!

hi rbigongi! welcome to pf!

force x time = change in momentum

force x distance = work done = change in energy​

if you apply the same force for the same distance, then yes the energy will be the same

but we usually talk about applying the same force for the same time

(the same impulse)