# Momentum

Momentum is the product of the mass and velocity of an object. If m is an object's mass and v is its velocity, then the object's momentum p is:

p = m v

Momentum is a vector quantity, having a magnitude and a direction.

One of the most powerful laws in physics is the law of momentum conservation, which 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 objects before the collision is always equal to the total momentum of the two objects after the collision:

m1v1+m2v2 = m1v'1+m2v'2

where m1 and m2 are the masses of object 1 and object 2, respectively, v1, v2 are the velocities of object 1 and object 2 before the collision, and and v1', v2' are the velocities of object 1 and object 2 after the collision.

The law of momentum conservation tells us that the momentum lost by object 1 is equal to the momentum gained by object 2.

A useful analogy for understanding momentum conservation involves a money transaction between two people. Let's refer to the two people as Maria and Will. Prior to the transaction, Maria possesses \$100 and Will possesses \$100. The total amount of money of the two people before the transaction is \$200. During the transaction, Maria pays Will \$50. Maria has lost \$50 and Will has gained \$50. The money lost by Maria is equal to the money gained by Will. After the transaction, Maria now has \$50 in her pocket and Will has \$150. Yet, the total amount of money of the two people after the transaction is still \$200.