** Momentum vs Velocity **

Momentum and velocity are two very basic concepts. These two concepts have remarkable similarities, but in theory, these are two different quantities. It is crucial to have a clear understanding in both velocity and momentum in order to excel in fields such as mechanics, automobile engineering, and almost every field in physics and engineering. This article will present the definitions of the two concepts, their uses, common laws and theories regarding them, their similarities and finally their differences.

**Velocity**

Velocity is a physical quantity of a body. The instantaneous velocity can be given as the instantaneous speed of the object with the direction the object is moving at that moment. In Newtonian mechanics, the velocity is defined as the rate of change of displacement. Both velocity and displacement are vectors. They have a quantitative value and a direction. The quantitative value alone of the velocity is called the modulus of velocity. This is equal to the speed of the object. The average velocity of an object is the difference between final and the initial velocity (in separate three dimensions) divided by the total time. The velocity of an object is directly related to the kinetic energy of the object. Using classical mechanics the kinetic energy of an object is half times mass multiplied by velocity squared divided. The theory of relativity suggests a more advanced version, which is not discussed here. The theory of relativity also suggests that the observed mass of an object increases when the velocity of the object is increased. The velocity of an object is dependent only on the changes of space time coordinate of the object.

**Momentum**

Momentum is a very important property of a moving object. The momentum of an object is equal to the mass of the object multiplied by the velocity of the object. Since mass is a scalar, the momentum is a vector, which has the same direction as the velocity. One of the most fundamental laws regarding momentum is Newton’s second law of motion. It states that the net force acting on an object is equal to the rate of change of momentum. Since mass is constant, on non-relativistic mechanics, the rate of change of momentum is equal to mass multiplied by the acceleration of the object. The most important derivation from this law is the momentum conservation theory. This states that if the net force on a system is zero the total momentum of the system remains constant. Momentum is conserved even in relativistic scales. It must be noted that the momentum is dependent on both the mass of the object and the space time coordinate change of the object.

• Momentum is dependent on mass, and velocity is independent of mass. • The momentum is conserved in a closed system, but the velocity is not conserved. • An external force is always required to change the velocity, but momentum can be changed by changing mass. |