Okay, this is something that's been bugging me for a long time, and I should have asked my physics teacher this past year way back when we were discussing mechanics, but I never could remember to do it. Let's say I have an identical twin, and we're both on a big frozen pond, standing still relative to the pond and the earth. I push him with a force F, and through Newton's 2nd law I'm pushed back with a force of F. He goes one way with velocity V, I go with velocity -V (relative to the earth). But what if he has special boots, or is nailed to the ground, or is stuck in the ice, or through whatever means is fixed to the earth? Would I still have velocity -V relative to the pond, or would it be -2V or something else entirely? Back when I first started turning this over in my head, I thought that I exert F on him (and he F on me from Newton's 2nd), but since he's attached to the ground, he exerts F on the ground, which exerts F on him, which gets transferred to me, which means 2F total is exerted on me, and I'd move backward at -2V. But I was thinking today about conservation of momentum... in the first scenario, since our masses are equal, our speeds would be equal, but in the opposite direction. But in the second scenario, the only difference is that I'm not just pushing him, I'm pushing him and the earth, which has a bit more mass and wouldn't have any significant change of motion - and I'd still have just the regular old F put back on me, and still move -V relative to the earth. Now my problem is that the first solution doesn't seem right with all the transfers of force and whatnot, but the second seems kind of counterintuitive since I'm exerting a force on the frame of reference itself, and it seems that my speed should be different because of the different setup. But since the frame (the earth) won't be moving much due to the force, it can still be used as a frame of reference... Sorry if this all sounds kinda confusing, it's hard to put into words, especially considering I've only had one year of high school physics, but I'm hoping someone here can shed some light on the subject... EDIT: It's the 3rd law, not the second... yeah, it's been a while for me.