Help answering momentum question Watch
The Law of Momentum Conservation states that if no external forces act on a system, then the system’s momentum will not change. If you treat the ball as your system, it is clear that the gravitational force is acting on the ball, provides an impulse, and therefore changes the ball’s momentum. But this is not a violation of the Conservation of Momentum because there is an external force acting.
The above answer to me seems correct, but sort of an 'easy way out'. Would a better answer be that as the ball moves down the hill due to the force of gravity it therefore has an impulse. But as gravity will attract the earth then so too does the earth. However this impulse will be hardly noticeable due to the large mass of the earth being so large. Therefore the law is conserved.
I would suggest that you start from Newton's Second Law.
If there is no externally applied force (F = 0) and there is no change in mass (), then you recover the classic .
In the case of a ball rolling down a hill, for simplicity, the only applied force is that of the weight of the ball parallel to the slope of the hill i.e. .
TLDR: There is an externally applied force of the ball's self-weight and thus the system is not a closed one. Hence, the Law of CoM is not valid.