Linear Momentum

What is Linear Momentum?

p = m * v

Momentum is a vector quantity that describes the motion of an object.
Momentum is always conserved, and does not change unless there is an external force.
The change in momentum is equal to the force applied.

The conservation of momentum is the most important principle to keep in mind when it comes linear momentum.
It states that in any collision or explosion momentum is conserved, provided that there are no external forces that have an effect.
This means that without any external forces acting on the system, the total initial momentum will always be equal to the total final momentum.

In physics, a collision is when two bodies come into contact with one another and exert forces on each other for a brief time.
There are two types of collisions, elastic and inelastic collisions.
In elastic collisions, both total momentum and total kinetic energy are conserved.
In inelastic collisions, only total momentum is conserved.
Depending on how much kinetic energy is lost, the collision is said to be "more inelastic" or "less elastic".

Momentum can be passed between objects during collisions, where one object loses the momentum they had, and the other gains it, meaning that total momentum is still conserved.

Another type of elastic collision is when two objects collide and change directions.

Sometimes when objects collide, they "stick" together and keep moving as a single mass.

As momentum is conserved, the momentum of the first and second object must equal their momentum when they are moving as one.
As they will be heavier, they are often slower when moving together.
As kinetic energy is described as Eₖ= 1/2(mv ²) , the reduction in velocity will actually lead to a reduction in kinetic energy, as velocity is squared.
Kinetic energy can be lost as it is converted into other types of energy, such as heat.

In physics, an explosion describes when two or more masses, which were initially at rest, are propelled apart from each other.
Momentum is still conserved in an explosion.
Considering that the objects are initially still, the momentum of the objects propelled away from each other must cancel out, so that the total momentum is still zero.
In an explosion, kinetic energy is increased, as masses that were still before now have velocity.
The kinetic energy increase comes as other forms of energy, such as chemical energy, are converted into kinetic energy.

For collisions or explosions in two dimensions, the law of conversation of momentum can be applied in two perpendicular directions.
After an explosion or collision, if the new momentum is in different angles, then the total momentum can be found by decomposing and adding and subtracting the vectors of momentum.
The total momentum should always stay the same before and after the collision or explosion.

Example

The most common equation for kinetic energy is Eₖ= 1/2(mv ²), however as momentum is described as p = mv, we can create a new equation.

Eₖ = p²/(2m)

This equation is useful for finding kinetic energy without having to separately calculate velocity.

Sources