Hello everyone, I've been going through my school's freshman physics course pretty smoothly, but momentum seems to be a difficult concept for me to master. I understand all the equations and how the variables relate to one another, but we've gotten to the law of conservation of momentum and a lot of extremely basic questions (that refer back to Newton's Third Law) are making me question my understanding. I'm not really understanding the conservation of momentum regarding the fact that "before" momentum is the same as "after" momentum. Is it a millisecond before the event? 2 minutes before event? Here's an example of a problem included in the lesson on momentum conservation (answer is shown on the website, but I'm just looking for further in-depth explanation): http://www.physicsclassroom.com/class/momentum/Lesson-2/Momentum-Conservation-Principle - (you can see all the question/answer sets if you scroll to the bottom :) ) #4: If a ball is projected upward from the ground with ten units of momentum, what is the momentum of recoil of the Earth? Do we feel this? Explain. This problem basically sums up what I was saying. How do I know if the ball was at rest and then thrown up (delta p would of course be 10 in this case) vs observing the ball right before and after the event? I remember doing a gun recoil example in class - my teacher said that when the bullet is fired, while the bullet does have a high velocity and therefore high momentum, the gun has a total momentum of 0 ? (is gun momentum+bullet momentum not >1?). So yes, the answer on the website says 10 units downward to match the upward momentum - but why? How would you express that in an equation/formula? Here's another one: #1: When fighting fires, a firefighter must use great caution to hold a hose that emits large amounts of water at high speeds. Why would such a task be difficult? I understand that by the third law, if the hose is pushing the water forward, the water must be pushing the hose back. But how does this relate to momentum conservation? How would you express the situation with variables like p, m, v, etc. (or would you not?) I have many more questions, but I don't want to spam, so this will be my last one: A clown is on the ice rink with a large medicine ball. If the clown throws the ball forward, then he is set into backwards motion with the same momentum as the ball's forward momentum. What would happen to the clown if he goes through the motion of throwing the ball without actually letting go of it? Explain. http://www.physicsclassroom.com/class/momentum/Lesson-2/The-Law-of-Action-Reaction-(Revisited) Okay, so momentum before the event is 0, correct? I also know that because he is going into backward motion with the same momentum as the ball's forward momentum (let b=ball and c=clown): pc=pb. But where do I go from there? I know they have the same change in momentum, but how would that explain what would happen if the clown "goes through the motion of throwing the ball without actually letting go"?