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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

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

Therefore, 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

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

At first, though, our momentum problems will be in only one dimension. We will imagine objects traveling in a straight line.

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 constant, then the momentum of an object is directly proportional to its velocity. In the example at the left, the mass is kept constant at a value of 2.0 kg. 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 the direct proportion between momentum and velocity.

That is, if one were to double the velocity of an object, then the momentum of
that object would also double. And, if one 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 constant, then the momentum of an object is directly proportional to its mass. In the example at the left, the velocity is kept constant at a value of 3.0 m/s. 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.

That is, if one were to triple the mass of an object, then the momentum of that object would also triple. And, if one 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.

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