| that's very interesting! but it's about angular momentum and I'm not confident that I can take the lesson over to linear momentum. Here's my caveman f=ma thought experiment: 1. make it 2-d. 2. replace the fan with a person sitting on a chair on a frictionless surface. 3. instead of air it's an endless field cinder blocks ahead of him. the person reaches out, and pulls in a cinder block. f=ma says they each move toward the other while the center of mass of the combination of them does not move. Now, if he throws the cinderblock behind him, he moves further forward - this would be analogous to an airplane propeller. or a fan in an open pipe. If he, um, splits the cinderblock in two and places each half directly off to his sides there is no net force exerted on him by this. This is the fan in a T-shaped pipe. the fan+pipe grabs air from ahead, moves this mass backward and then sets it aside. it's not a jet-engine, but it is moving the air mass toward itself and must be moved equally and oppositely. I don't think it's essential to worry about how the air/blocks rearrange themselves after this - but if the blocks surround and jostle, that's just another effect layered in super-position over this one, and if we don't agree so far then it will only make things more confusing |
With your concrete block example, as I start pulling the block towards me I experience an impulse forward. But when it approaches my body I slow it down to zero speed, creating an opposite impulse. So although I might have moved forward a few inches during the motion, my momentum is zero at the end. When you scale this up to large numbers of air molecules, the result is the same.