Importance of Momentum.

Momentum is a corner stone concept in Physics. It is a ** conserved quantity**. That
is, within a closed system of interacting objects, the

This allows you to calculate and predict outcomes when objects bounce into one another. Or by knowing the outcome of a collision, you can figure out what was the initial state of the system.

The type of momentum which we will be covering here is called **
linear momentum**. In classical physics this is the momentum
of a mass (an object) as it moves along a straight line.

Momentum is mass times velocity.

When an object is moving, it has a non-zero momentum. If an object is standing still, then its momentum is zero.

To calculate the momentum of a moving object multiply the ** mass** of the object

A sample momentum calculation.

In the above picture, let's say that the mass is 2.0 kg and that the velocity is 4.0 m/s. That is:

m = 2.0 kg

**v **= 4.0 m/s

To calculate the momentum for this object we will multiply the mass times the velocity:

**p**= m**v**

**p**= (2.0 kg)(4.0 m/s)

**p**= 8.0 kg-m/s

So, the momentum of the object is calculated to be 8.0 kg-m/s.

Note the
unit for momentum. It is ** 'kg-m/s'**. This is pronounced

Momentum is a vector.

Momentum is a
** vector**. That means that momentum is a quantity that has a

The above problem is a
** one dimensional problem**, so the object is moving along a

So, in the above problem you would say that the momentum is **
'positive 8.0 kg-m/s'**, or

If the object was moving toward the left with a velocity of -4.0 m/s,
then the momentum would be -8.0 kg-m/s, and you would say **
'negative 8.0 kg-m/s'**.

Momentum problems can become more complicated, however.
You can calculate momentum in two and three dimensions. Under these
conditions, say in a two dimensional problem, you would state a momentum
using language such as ** '3.0 kg-m/s in a direction of 50 degrees
North of East'**.

At first, though, our momentum problems will be in only one dimension. We will imagine objects traveling in a straight line moving toward the right (positive) or left (negative).

Momentum is not velocity.

Sometimes the concept of ** momentum** is confused with the concept of

Momentum is directly proportional to velocity.

If the
** mass** is kept

The velocity changes from 0 m/s to 10 m/s while the momentum changes from 0 kg-m/s to 20 kg-m/s. This creates a straight line graph when momentum is plotted as a function of velocity. (The symbol for momentum as a function of velocity would be p(v).) The straight line graph demonstrates a direct proportion between momentum and velocity.

So if you were to double the velocity of an object, then the momentum of that object would also double. And, if you were to change the velocity of an object by a factor of 1/4, then the momentum of that object would also change by a factor of 1/4.

Momentum is directly proportional to mass.

If the
** velocity** is kept

The mass changes from 0 kg to 10 kg while the momentum changes from 0 kg-m/s to 30 kg-m/s. This creates a straight line graph when momentum is plotted as a function of mass. (The symbol for momentum as a function of mass would be p(m).) The straight line graph demonstrates the direct proportion between momentum and mass.

For example, if you were to triple the mass of an object, then the momentum of that object would also triple. And, if you were to change the mass of an object by a factor of 1/2, then the momentum of that object would also change by a factor of 1/2.