Momentum is a vector quantity (with both magnitude and direction) that describes the amount of motion that an object has. The linear momentum for an object traveling a straight path is equal to the product of the object's mass and velocity. The total momentum of a system is given by the vector sum of the momenta (plural of momentum) of each of the objects involved. For example, when a cannon fires a cannonball, the total momentum of the system is equal to the momentum of the cannon plus the momentum of the cannonball.

In a closed system—a system with no outside forces acting on it—momentum is conserved; in other words, the total amount of momentum always remains the same. Before the cannonball is fired, both the cannon and the ball are at rest; the momentum of each of the objects is zero and therefore the total momentum of the system is zero. After the ball is fired, the ball possesses momentum in the direction it travels. However, if we assume that the cannon and cannonball are in a closed system (although, in reality, they are not), the total momentum of the system must be conserved and therefore still equals zero—which means that the cannon must recoil. In order for the total momentum of the system to equal zero, the cannon must have momentum equal in magnitude and in the opposite direction of the ball.

Conservation of momentum can be used to predict the motions of objects in a system. For example, given that momentum is equal to the product of an object's mass and velocity, if the momentum of the cannon is equal in magnitude to the momentum of the ball, the massive cannon must move at a smaller velocity than the less massive ball.

Similarly, the collision of carts on an air track also demonstrates the conservation of momentum. The air track provides a cushion of air under the carts, which allows them to glide freely without the force of friction acting significantly on them. As a good approximation of a closed system, the principle of momentum conservation applies: the sum of the momenta of the carts before and after the collision must be equal.

For example, imagine a moving cart colliding with a cart at rest on an air track. The stationary cart has zero momentum; therefore, the total momentum of the system is equal to the initial momentum of the moving cart. After the collision, whether it is an elastic collision (kinetic energy is conserved and the carts bounce off each other) or an inelastic collision (the carts stick together after the collision as a single mass), the total momentum of the system will always equal the initial momentum of the first moving cart.

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