Think of momentum as an object's resistance to stop. If a train is moving with a velocity it has a bigger momentum than a biker moving at the same velocity. read more
In Newton’s cradle for example, the outermost ball has some momentum that it passes through the other balls, when it reaches the ball at the other end, it bounces off (because it has nowhere else to pass the momentum so it resorts to motion) and repeats the chain. read more
The train has a lot of momentum when it starts moving because it is hard to stop it so it's tendency to keep moving or keep still is very high. This concept is very useful as well in order to improve optimization algorithms. read more
I'm having a fairly hard time understanding the intuition behind Noether's derivation of the conservation of angular momentum from the rotational invariance of the Lagrangian, though I do understand it mathematically, I just don't get it intuitively. read more