I've taken up to the equivalent of first year undergrad mechanics, but this simple concept is unclear to me. Say a force F is applied (perpendicular) to a rod (in a vacuum with no gravity-- F is the only external force) at a non center of mass point A for a tiny time dt. How does it move? My thoughts: Its CM accelerates with a = F/m. A force on an object is a force on an object regardless of where-- Newton's 2nd Law applies. There is also some rotation. That's what I don't understand well. There is rotation with respect to any point except A. Say I pick the CM. The torque applied with respect to the CM is τ = rF where r is the distance between the point A and the CM. Then the final angular momentum with respect to the CM can be found from τ = dL/dt. But say I pick a different point, like point A itself. Then r is different (in the case of point A, r = 0), and the final angular momentum is different (in this case 0) with respect to that point. Which value of L is correct? The point I choose shouldn't matter, should it? Also, further thought makes be think that my first thought is false (it will not necessarily accelerate with a = F/m). What if F was applied at the tip of the rod? Then the rod would spin much more than it would linearly accelerate. If you could explain how to analyze this situation with kinematics, momentum, and energy, that would be very helpful. Or at least (first) help me understand it with kinematics and momenta.