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In addition to the revision notes for Law of Conservation of Momentum and Kinetic Energy on this page, you can also access the following Centre of Mass and Linear Momentum learning resources for Law of Conservation of Momentum and Kinetic Energy

Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
---|---|---|---|---|---|---|

6.2 | Law of Conservation of Momentum and Kinetic Energy |

In these revision notes for Law of Conservation of Momentum and Kinetic Energy, we cover the following key points:

- What is the Law of Conservation of Momentum?
- In which situations the Law of Conservation of Momentum is applied?
- The meaning of the Law of Kinetic Energy Conservation
- What are the limitations of the Law of Kinetic Energy Conservation?
- How to use the Laws of Conservation in calculating any missing velocity or mass

The **Law of Conservation of Momentum** for two colliding objects says that:

**"The total momentum prior to the impact for two objects involved in a collision process is always equal to their total momentum after the impact, regardless the type of collision."**

The mathematical expression of the Law of Conservation of Momentum for two objects (1) and (2) colliding elastically, is

p*⃗*_{01} + p*⃗*_{02} = p*⃗*_{1} + p*⃗*_{2}

or

m_{1} × v*⃗*_{01} + m_{2} × v*⃗*_{02} = m_{1} × v*⃗*_{1} + m_{2} × v*⃗*_{2}

where m_{1} and m_{2} are the objects' masses, v_{01} and v_{02} are their respective initial velocities prior to collision and v_{1} and v_{2} are their velocities after the collision.

When the collision is inelastic, the Law of Conservation of Momentum is written as

m_{1} × v*⃗*_{01} + m_{2} × v*⃗*_{02} = (m_{1} + m_{2}) × v*⃗*

where v*⃗* is the common velocity of the two objects after the collision as they move together.

As for kinetic energy, it is conserved only in perfectly elastic collisions. The equation that represents mathematically the Law of Conservation of Kinetic Energy is

The two abovementioned laws are very fundamental in mechanics and they are known as the "Laws of Conservation".

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