Linear Momentum: Relation with 2nd Law of Newton

Abstract

Momentum is the quantity of motion due to its mass and velocity. Mathematically expressed as p=mv with SI unit newton second Ns. When a force acts on a body, it produces an acceleration in the body and will be equal to the rate of change of momentum of the body.

It can be written as F x t=m v_f -m v_i. The change in momentum amounts to the product of force and the time for which force is applied. This kind of second law is more general than the  F =ma since it can easily be extended to deal with changes as the body accelerates.

The momentum of a system depends upon its mass and velocity. If no unbalanced or net force acts upon a system, then its momentum remains constant. Therefore, this is the conservation of momentum.

Definition of Momentum

The momentum of a body is the quantity of motion it has due to its mass and velocity.

We understand the fact that moving item possesses a quality by means of which it puts in a force on anything that tries to stop it. The faster the object is moving, the more difficult is to stop it. Similarly, if two items move at the exact same speed, then it is more difficult to stop the massive of the two.

This quality of the moving body was called the quantity of motion of the body, by Newton. This term is now called linear momentum of the body and is specified by the relation.

Mathematical Form

Linear momentum = p = mv

ln this expression, v is the speed of the mass m. Direct momentum is, therefore, a vector quantity and has the direction of speed.

SI Unit

The SI unit of momentum is kg metre – per second (kgms^-1). It can likewise be expressed as newton second(Ns).

Momentum and Newton’s Second Law of Motion

Statement

When a force acts on a body, it produces an acceleration in the body and will be equal to the rate of change of momentum of the body.

Explanation

Consider a body of mass m moving with an initial velocity v_i. Suppose an external force F acts on it for time t after which velocity ends up being v_f. The acceleration produced by this force is given by

                 a = v_f – v_i / t

By Newton’s 2^nd law of motion acceleration, a is

                            a = F/m

Comparing the two values of acceleration

F/m= v_f – v_i / t

Now,

F x t=mv_f -mv_i

Where

• m v_{i –>} initial momentum
• mv_{f –>} final momentum

The change in momentum amounts to the product of force and the time for which force is applied. This kind of the second law is more general than the type F =ma since it can easily be extended to account for changes as the body accelerates when its mass also alters. For example, as a rocket speeds up, it loses mass because its fuel is burnt and ejected to offer higher thrust.