# 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:

m_{1}v_{1}+m_{2}v_{2} = m_{1}v'_{1}+m_{2}v'_{2}

where *m _{1}* and

*m*are the masses of object 1 and object 2, respectively,

_{2}*v*,

_{1}*v*are the velocities of object 1 and object 2 before the collision, and and

_{2}*v*,

_{1}'*v*are the velocities of object 1 and object 2 after the collision.

_{2}'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.