Say you've got a dumbbell-type object sitting still in space, and a mass comes in from below and strikes it. We've got a collision. If the mass strikes the dumbbell away from the center of mass, then it will cause the dumbbell to do two things (1) rotate, (2) the center of mass will move up. My question is, does the location at which the incoming mass strikes the dumbbell have any effect on the subsequent center of mass motion? I know that striking further from the center of mass means the incoming projectile starts with rotational momentum, which is conserved, so the rotation is greater. But if I'm not mistaken, the COM motion only cares about linear momentum, not rotational, so that it wouldn't matter where on the object you strike it, the center of mass will always respond in the same way. But then I get tripped up because this would mean that you can start with the same amount of energy in your incoming projectile, and get a more or less violent response from the collision simply from changing the geometry, which seems sort of like it would be violating energy conservation? Does the discussion change it all for elastic, as compared to inelastic collisions? Thanks.