Momentum and Its Conservation

Momentum refers to the quanity of motion that an object has.
Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, than it has momentum-it has its mass in motion. The amount of momentum which an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity. In terms of an equation, the momentum of an object is equal to the mass of the object times the velocity of the object.
Momentum = mass • velocity
In physics, the symbol for the quantity momentum is the lower case "p". Thus, the above equation can be rewritten as
p = m • v
Where m is the mass and v is the velocity. The equation illustrates that momentum is directly proportional to an object's mass and directly proportional to the object's velocity.
The units for momentum would be mass units times velocity units. The standard metric unit of momentum is the kg•m/s.
Momentum is a vector quantity
Momentum and Impulse Connection:
These concepts are merely an outgrowth of Newton's second law. Newton's second law (Fnet = m • a) stated that the acceleration of an object is directly proportional to the net force acting upon the object and inversely proportional to the mass of the object. When combined with the definition of acceleration (a = change in velocity / time), the following equalities result.
F = m * a = m * v/t or F = m * v/t
If both sides of the above equation are multiplied by the quantity t, a new equation results.
F * t = m * v
To truly understand the equation, it is important to understand its meaning in words. In words, it could be said that the force times the time equals the mass times the change in velocity. In physics, the quantity force • time is known as impulse. And since the quantity m•v is the momentum, the quantity m• v
must be the change in momentum. The equation really says that the Impulse = Change in momentum
The physics of collisions are governed by the laws of momentum.
In a collision, an object experiences a force for a specific amount of time which results in a change in momentum. The result of the force acting for the given amount of time is that the object's mass either speeds up or slows down (or changes direction). The impulse experienced by the object equals the change in momentum of the object. In equation form, F • t = m• v.
Momentum Conservation Principle
One of the most powerful laws in physics is the law of momentum conservation. The law of momentum conservation can be stated as follows.
For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objec~s before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object I is equal to the momentum gained by object 2.
The above statement tells us that the total momentum of a collection of objects (a system) is conserved - that is, the total amount of momentum is a constant or unchanging value ..
Isolated Systems
Total system momentum is conserved for collisions occurring in isolated systems. But what makes a system of objects an isolated system? And is momentum conserved if the system is not isolated?
A system is a collection of two or more objects. An isolated system is a system which is free from the influence of a net external force which alters the momentum of the system. There are two criteria for the presence of a net external force; it must be ...
a force which originates from a source other than the two objects of the system
a force that is not balanced by other forces.
A system in which the only forces which contribute to the momentum change of an individual object are the forces acting between the objects themselves can be considered an isolated system.
If a system is not isolated, then the total system momentum is not conserved. Because of the inevitability of friction and air resistance in any real collision, one might conclude that no system is ever perfectly isolated. The reasoning would be that there will always be a resistance force of some kind robbing the system of its momentum
Momentum Conservation in Explosions
For collisions occurring in isolated systems, there are no exceptions to this law. This same principle of momentum conservation can be applied to explosions. In an explosion, an internal impulse acts in order to propel the parts of a system (often a single object) into a variety of directions. After the explosion, the individual parts of the system (which is often a collection of fragments from the original object) have momentum. If the vector sum of all individual parts of the system could be added together to determine the total momentum after the explosion, then it should be the same as the total momentum before the explosion. Just like in collisions, total system momentum is conserved.