In classical mechanics, linear momentum, or translational momentum, is simply the product of the mass and the velocity of an object. Like velocity, linear momentum is a vector quantity which means that it possesses magnitude as well as direction. This can be shown by the equation:
p = mv
Where p is linear momentum, m is the mass of the object, and v is the velocity of the object. The bold of the p and v indicates that they are vector quantities.
Linear momentum is also a conserved quantity, similar to energy. This means that in a closed system (no external forces acting on the system) the total linear momentum cannot change. This also applies to systems of many particles where instead of just p=mv, it is the sum of all of the particles momenta. For example, in a system of two particles the momentum with masses m1 and m2 and velocities v1 and v2, the total momentum is:
p = m1v1 + m2v2
Linear momentum also has a strong relationship with the force applied to the object. If a force, F, is applied to an object for a time interval, Δt, the momentum of the object changes according to this equation:
Δp = F Δt
Viewed in its differential form, F = dp/dt, Newton’s second law is shown: The rate of change of the momentum of a particle is equal to the force acting on it.
Collisions: Elastic versus Inelastic
An elastic collision is such that no kinetic energy is lost. Simply put, the total kinetic energy of the two colliding bodies remains constant. In addition, the total momentum of the two objects does not change either. An example of this would be when bouncing a ball off of a wall. In an inelastic collision however, some kinetic energy is lost and converted into other forms of energy such as heat or sound. There is also a special case known as a perfectly inelastic collision in which both bodies have the same motion after the collision. An example of an inelastic collision would be when two or more cars collide with one another.
This article was written for you by Troy, one of the tutors with Test Prep Academy.