Newton's Laws of Motion are three physical laws in classical mechanics which state the following:

1. A body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force. ^first-law
2. At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass. ^second-law
3. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. ^third-law

Relation to Momentum

Newtons 3 laws can be thought of in an inertial frame of reference as describing the different laws of momentum. The 3 laws can be thought of as describing the following phenomena:

1. The momentum of a closed system is conserved
2. The change in momentum directly related to the force acting upon an object
3. Momentum is transferred equally between two objects when they collide.

Equations of Newtons Laws

Newtons laws can be quantified using the following equations

Newton's Second Law

Newtons second law relates the force acting upon an object to it's acceleration and mass. This relationship is described using the following equation

Where is the total force acting upon an object from all sources

Noticing that acceleration is the derivative of velocity with respect to time we can re-write this equation to find the relation between force and momentum.

We can now see the relationship between force and the change in momentum.

Newton's Third Law

Newton’s third law describes how forces, and therefore momentum are exchanged between interacting objects. When two objects collide or interact, each exerts a force on the other.

In the following equations describes the quantity being "transferred" from object to object whereas is the reverse.

According to the third law, these forces are equal in magnitude but opposite in direction:

again via the relationship shown in the second law this can be re-written to show the relation to the transfer of momentum