Today in class we learned about how if a force F is applied to a dumbbell on its center of mass and then separately applied to the edge where it gets its maximum torque, the dumbbell will have the same CM velocity after. It makes sense when you think about it in terms of momentum. F times T gives the impulse and so it is the same in both cases. I get confused about its energy. The second case has more energy because it is rotating and translating.....makes sense, BUT how can a force applied for a certain time give something more energy when it is applied to a different position? Also, in my mind I imagine the force being applied to the dumbbell in case 2 and it just rotates around that point because there is maximum torque. Obviously my thoughts are flawed, would anyone care to explain why? If you can provide mathematical proof that'd be great!! EDIT: If I flick my pen at its center of mass, it goes across the table really fast, but if I flick it at the end, it spins and only has a minor transnational velocity. That seems counter intuitive to what my teacher said.