# Law of Conservation of Momentum and Kinetic Energy

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6.2Law 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

## Law of Conservation of Momentum and Kinetic Energy Revision Notes

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

p01 + p02 = p1 + p2

or

m1 × v01 + m2 × v02 = m1 × v1 + m2 × v2

where m1 and m2 are the objects' masses, v01 and v02 are their respective initial velocities prior to collision and v1 and v2 are their velocities after the collision.

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

m1 × v01 + m2 × v02 = (m1 + m2) × 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

m1 × v201/2 + m2 × v202/2 = m1 × v21/2 + m2 × v22/2

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

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