My name is Alexander Fufa

**eV**and here I will explain the following topic:# Conservation of Momentum

## Formula

## What do the formula symbols mean?

## Velocity of the first body (before)

`$$ \class{red}{v_1} $$`Unit

`$$ \frac{\mathrm m}{\mathrm s} $$`

Velocity of the first body before the collision with the second body. The first body has the momentum \( p_1 = m_1 \, v_1 \).

## Velocity of the second body (before)

`$$ \class{blue}{v_2} $$`Unit

`$$ \frac{\mathrm m}{\mathrm s} $$`

Velocity of the second body before the collision with the first body. The second body has the momentum \( p_2 = m_2 \, v_2 \).

## Mass of the first body

`$$ m_1 $$`Unit

`$$ \mathrm{kg} $$`

Here it is assumed that the mass of the first body remains the same before and after the collision.

## Mass of the second body

`$$ m_2 $$`Unit

`$$ \mathrm{kg} $$`

Here it is assumed that the mass of the first body remains the same before and after the collision.

## Velocity of the first body (after)

`$$ \class{red}{v'_1} $$`Unit

`$$ \frac{\mathrm m}{\mathrm s} $$`

Velocity of the first body after the collision with the second body.

## Velocity of the second body (after)

`$$ \class{blue}{v'_2} $$`Unit

`$$ \frac{\mathrm m}{\mathrm s} $$`

Velocity of the second body after the collision with the first body.

**Explanation**

## Video

**Conservation of momentum** is one of the laws of conservation in physics and applies when no force acts on a particle:

Formula anchor
$$ \begin{align} \boldsymbol{F} = 0 \end{align} $$

The Newton's 2nd law states the following:

Formula anchor
$$ \begin{align} \boldsymbol{F} = \frac{\text{d}\boldsymbol{p}}{ \text{d}t } \end{align} $$

With Eq. 1

the time derivative of the momentum disappears:

Formula anchor
$$ \begin{align} 0 ~=~ \frac{\text{d}\boldsymbol{p}}{ \text{d}t } \end{align} $$

If the pulse does not change over time, it is constant:

Formula anchor
$$ \begin{align} \boldsymbol{p} = \boldsymbol{p}_0 = \text{const.} \end{align} $$