Is the law of momentum conservation violated when a ball rolls down a hill and gains momentum?
The law of conservation of momentum states that the *total momentum* of all interacting bodies remains constant regardless of the applied forces between the bodies. In your case, imagine the linear and angular momentum of the ball. By Newton’s third law, there is an opposite reaction somewhere else. Given the momentum vectors the ball has at any time: P(t) and L(t), the earth, air molecules,hill molecules,etc are moving and rotating in opposite directions: -P(t) and -L(t). If we had a way to sum all these “little vectors” we would find: ∑P and ∑L =0 according to the law. Answer: The law is not violated. Edit: free fall—> linear momentum: During a free fall, the earth and ball are reacting with each other via gravity: mb vb(t) = Me ve(t). ve(t) is negligible, but not zero. Momentum is still conserved.
