Linear momentum (SI unit kg m/s, or Ns) is a vector quantity, possessing a direction as well as a magnitude.
P = m v
Linear momentum is a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. Conservation of linear momentum is implied by Newton’s first law.
Newton’s laws of motion
Newton’s laws of motion are the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces.
The First law is summarized as follows:
If there is no net force on an object, then its velocity is constant. The object is either at rest (if its velocity is equal to zero), or it moves with constant speed in a single direction.
The first law can be stated mathematically as
∑ F = 0 => dv / dt = 0
Consequently, an object that is at rest will stay at rest unless an external force acts upon it.
An object that is in motion will not change its velocity unless an external force acts upon it.
Newton’s second law:
The second law states that the net force on an object is equal to the rate of change (that is, the derivative) of its linear momentum p in an inertial reference frame:
F = dp / dt = d(mv) / dt
The second law can also be stated in terms of an object’s acceleration. Thus,
F = m dv/dt = m a
where m is the mass of the body, and a is the body’s acceleration.
Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it.
An impulse J occurs when a force F acts over an interval of time Δt.
J = ∆p = m ∆v
Impulse is a concept frequently used in the analysis of collisions and impacts.
Newton’s third law
The third law states that all forces exist in pairs: if one object A exerts a force FA on a second object B, then B simultaneously exerts a force FB on A, and the two forces are equal and opposite:
FA = −FB