|In class, you sat motionless on a cart with a ball in your lap. You said that your momentum was zero. You then threw the ball in one direction and you began moving in the other direction. You said that your momentum was still zero. How can your momentum be zero if you are moving?
In both cases, I was referring to the total momentum of the ball and me. The total momentum of the ball and me was zero before I threw the ball and it was still zero after I threw the ball. However, before I threw the ball nothing was moving and after I threw the ball the two of us were moving in opposite directions. It was our total momentum that was zero after the throw, not our individual momenta. While the ball and I each had a nonzero momentum after the throw, our momenta were equal in amount but opposite in direction—the ball's momentum was exactly opposite mine. If you were to add our momenta together, they would sum to zero. Since momentum is conserved and we couldn't exchange momentum with anything around us, the ball and I began and ended with the same total amount of momentum: zero.