# Conservation of momentum

## Terminology

Recall that momentum is a vector property of a moving object. It is a scalar multiple of the velocity of the object, that is

$$\textbf{momentum} = \textbf{mass} \;\,\text{times} \;\,\textbf{velocity}.$$

The important property of momentum is that it is conserved in collisions. That is, when objects collide, the total momentum before collision is equal to the total momentum after collision. Figure 1: Elastic collision: The momentum of each ball is represented with the green arrows.

## Key equations

\begin{aligned} \text{Initial Momentum} &= \text{Final Momentum} \\ m_{1}v_{1i} + m_{2}v_{2i} &= m_{1}v_{1f}+m_{2}v_{2f} \end{aligned} \begin{aligned} \text{Initial Kinetic Energy} &= \text{Final Kinetic Energy} \\ \frac{1}{2}m_{1}v_{1i}^{2} + \frac{1}{2}m_{2}v_{2i}^{2} &= \frac{1}{2} m_{1}v_{1f}^{2} + \frac{1}{2} m_{2} v_{2f}^{2} \end{aligned}

## Simulation

Use the following simulation to explore the conservation of momentum. In the simulation we asume that the collisions are elastic, that is, the total kinetic energy of the two bodies after the collision is equal to their total kinetic energy before the collision.

Things to try:

• You can drag points A and B to change the position of the balls.
• Activate the box Axes to help you set the position of the balls.
• Change the velocity by activating Velocity box.
• Change the mass (kilograms) of the balls by dragging the sliders m1 and m2.
• Activate the Momentum box to show vectors.

Sorry, the simulation is not supported for small screens.