Law of conservation of linear momentum

Introduction

The linear momentum of a particle is also known as the product of the mass of the particle and the velocity of that particle. It is a vector quantity. Conservation of linear momentum is an essential principle in physics and other sciences. For example, when a ball is thrown horizontally into the air, the linear momentum gained by the ball must cancel out the linear momentum lost by the thrower.

Also, like massless particles, they cannot be destroyed but only change forms. A famous example of this behaviour is a collision between two billiard balls on a pool table: The balls experience a change in their linear momentum resulting from their interaction with each other. Momentum is represented by →  p

Conservation of Linear Momentum

According to the law of conservation of linear momentum, the net velocity of a system of bodies remains constant if no net external force acts on it. 

This is a particular case of a more general law: The net change in the energy of a closed system is equal to the sum of the external work done on it and its evolution in internal energy. Momentum is not an exact analogue of power, but for many practical situations, it behaves similarly; therefore, we can draw useful analogies between them. In particular:

Energy is a scalar quantity that has magnitude but no direction. Momentum is a vector quantity that has both magnitude and direction. If the net external force being acted on a system of bodies is precisely zero, then the system’s momentum always remains constant.

Conservation of Linear Momentum Formula

The principle of conservation of linear momentum says that if two objects collide, then the total momentum before and after the collision will always be the same if no other external force is acting on the colliding objects.

The law is accepted as being a fundamental physical law. It holds in all cases, from subatomic to galactic scales. For example, based on experimental evidence available at the time, the conservation of momentum is one of three basic conservation laws (the other two being the laws of energy and angular momentum conservation).

Conservation of linear momentum formula is essential in physics, especially in the collision problem. The protection of linear momentum depends on the system’s centre of mass and the net external force.

The formula for conservation of linear momentum is given as:

Initial Momentum= Final Momentum

Pi= Pf

The Linear Momentum formula can be expressed as-

P = mv

P is also known as the Linear Momentum.

v is also known as the Linear Velocity.

And m is the mass of the body.

Conservation of Linear Momentum Equation

The law of conservation of momentum states that in an isolated system, the total momentum of the system is constant. In other words, if no external force is acting on the closed system, the total momentum within the system remains constant. This means that the total of all the kinetic energy plus potential energy within the system is always equal to zero. Momentum is calculated by multiplying the mass by velocity; therefore, a closed system will have zero acceleration if its total momentum is conserved.

The law of conservation of momentum can also be easily explained from Newton’s second law of motion. Newton’s second law of motion states that the rate of change of the linear speed of a body is always equal to the net external force applied to it. Therefore, there must be no net external force acting on a body and thus causing it to change its momentum; there must be no friction or external pressure working on it.

It can be mathematically expressed by-

  dPdt  =  d(mv)dt

           = mdvdt

           =  ma

           =  Fnet

In physics, momentum is the mass of an object times its velocity. The net external force acting on a body is the sum of all forces acting on it, minus the sum of all forces acting due to gravity. If the net external force working on a body is zero, then the total rate of momentum change is also zero, which means that there is absolutely no change in the momentum.

Conservation of Linear Momentum Example

We can find it by using momentum conservation. Momentum is conserved for the two-body system. So if we add up the momentum of all the bodies before and after the collision, they will be the same.

Now let’s look at just one body of mass m moving with velocity v to which another body of mass M(initially at rest) collides. The total momentum before the collision is p = mv. After the collision, the total momentum is p’ = (m+M)v’. We know that p’ = p, and so we get an equation relating (m+M)v’ to mv :

This is a critical equation because it relates a change in momentum to a change in mass. It tells us that if we have an object of mass m moving with velocity v, then if we add a second object of mass M, the final velocity will be mvm+M. This may seem obvious, but you might have expected that they would keep their different speeds, or that they wouldn’t move at all, or something even more bizarre. So this relation between change in mass and change in velocity is worth remembering.

Applications of Conservation of Linear Momentum

Conservation of momentum is a fundamental law of physics that deals with the relationship between an object’s mass and velocity. This principle can be derived from Newton’s laws of motion; in fact, conservation of momentum extends Newton’s second law of motion.

One of the most critical applications of conservation of momentum is the launching of rockets. The rocket fuel burns are pushing the exhaust gases downwards, and because of this, the missile also gets a push upwards. Motorboats are also working on the same principle. It moves the water backwards and, as a result, gets pushed forwards in reaction to conserving momentum.

Traction applied to one side wheels or revolving axis causes a moving body like a bicycle to move forward. The same principle applies in a car where wheels push and pull the vehicle forward or backward under control by steering wheels.

Conservation of momentum states that if two bodies collide, their relative velocities before will be equal to their relative velocities after the collision. So, for example, it means that if two cars are moving towards each other at 20 mph, then after the collision, both will move away at 20 mph from each other.

Tension is a force that can be used to pull things together. For example, a propeller pulls water backwards in a thrusting motion in motorboats. When you put water in action, it tries to maintain its velocity. The propeller uses this principle to propel the boat forward by applying a backward force on the water.

Conclusion 

According to Conservation of linear momentum, if no net external force is acting on a body or a system of bodies then its net linear momentum remains constant. This concept is used to solve many problems, like that of rocket propulsion. The law of conservation of linear momentum can be easily related to Newton’s second law of motion.

dPdt = Fnet  is the mathematical way to relate the two laws.