Is Momentum Conserved In An Isolated System:Why,When And Detailed Facts And FAQs

When a system of particles is isolated from the rest of the world, the total momentum of the system is conserved. In this article, we will see how is momentum conserved in an isolated system.

The conservation of momentum law is derived from the second and third laws of motion, respectively. The overall momentum of the system has always been conserved in an isolated system. The forces in nature are internal to the system and add up to zero for the entire system. Because the external force on the system is zero, the system’s momentum is conserved.

We will discuss the following points in this article:

is momentum conserved in an isolated system

Image Credits: No-w-ay in collaboration with H. Caps, BillardCC BY-SA 4.0

Momentum may be defined as the quantity of motion experienced by a body under consideration. The momentum of a body is defined mathematically as a function of its mass and the velocity at which it is traveling, respectively. Generally, the isolated system isn’t very precise, but it usually covers the bodies that are being looked at.

Read more on Is Momentum Conserved: When, Why, How, Detailed Facts And FAQs

Now, let us see in detail about how is momentum conserved in an isolated system.

In an isolated system when is momentum conserved?

All of the time, it is conserved in any scenario.

Conserved does not always imply constant. It expresses the fact that something cannot be produced or destroyed at any moment. The condition in which a system is exposed to an external force net force, the momentum of the system changes, but it is conserved. Hence, everything about it is conserved at all times, in all situations.

Why is momentum conserved in an isolated system?

In this case, when there is no force from outside of the body system, the system is referred to as an isolated system.

According to Newton’s second law of motion, because no external force occurs on the system, The change in momentum is equal to zero; hence, the linear momentum is conserved.

dP/dt = 0

Henceforth, |P|= constant, (as derivative of a constant function is 0)

(In which P=mv=linear momentum is used)

The entire linear momentum of an isolated system, that is, a system that is not subjected to any external forces, is conserved.

Illustration on is momentum conserved in an isolated system

Frequently Asked Questions (FAQ’s)

Q. What do you mean by linear momentum?

Ans: For the sake of simplicity, Linear Momentum is used to grasp the quantitative idea of motion.

 The linear momentum is a measure of motion that quantifies both velocity and mass. It is defined mathematically as the product of mass and velocity.

It is represented as follow

P = mv

Where, P = Linear momentum

m= mass and v = velocity

Q. What is angular momentum?

Ans: In simple words, it is the momentum of rotating objects.

The term “momentum” refers to the product of the object’s mass and its velocity. Momentum may be found in any object that is moving with mass. The main difference between angular momentum is that it deals with revolving or spinning things.

It is represented as follow

L = mvr

Where, L = Angular momentum

m= mass, v= velocity and r = radius

Q. What do you imply when you speak of conservation of momentum?

Ans: Conservation means no change in the system or one can say that the initial or final value remains the same. The conservation of momentum law could be stated as follow:

“For two or more bodies in an isolated system acting upon each other, their total momentum remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed.”

Read more on 17 Momentum Example: Detailed Insight

Q. What is the formula of law of conservation of momentum and what are examples of it?

Ans: The law of conservation of momentum can be represented as follow:


The masses of the bodies are denoted by m1 and m2, and the initial velocities of the bodies are denoted by u1 and u2. The final velocities of the bodies are represented by v1 and v2.

Examples of conservation of momentum are given as follow:

  • The collision of two balls or cars
  • The rocket thrust
  • Newton’s cradle

With the help of Newton’s cradle, you can see how the balls in a row of balls will push forward when one ball is raised and then let go of the ball at the other end of the row.

is momentum conserved in an isolated system
Newtons Cradle

Image Credits: The Dean of PhysicsNewtons CradleCC BY-SA 4.0

Q. In the background, there are automobiles with weight of 5 kilogrammes and 6 kilogrammes, respectively. An automobile with a mass of 5 kg is moving at a velocity of 4 m.s-1 in the direction of the east. Calculate the velocity of an automobile with a mass of 6 kg in relation to the ground.

Ans: Given,

m1 = 5 kg, m2 = 6 kg, v2 = 4 m.s-1, v1 = ?

According to the rule of conservation of momentum, we can say that

Pinitial = 0, because the automobiles are at rest

Pfinal = p1 + p2

Pfinal = m1.v1 + m2.v2

= (5 kg). v1 + (6 kg).  (4 m.s-1)

Pi = Pf

0=(5 kg). v1 + 24 kg.m.s-1

v1 = 4.8 m.s-1

Q. Sedans of 100 kg and 200 kg mass are at rest. A 200 kilogramme car travelling at 60 m.s-1towards the west. Find the car’s velocity relative to the land.

Ans: Given,

m1 = 100 kg, m2 = 200 kg, v2 = 60 m.s-1, v1 = ?

When we look at the law of momentum, we can see that it holds true that,

Pinitial = 0, as the sedans are at rest

Pfinal = p1 + p2

Pfinal = m1.v1 + m2.v2

= (100 kg). v1 + (200 kg).  (60 m.s-1)

Pi = Pf

0=(100 kg). v1 + 12000 kg.m.s-1

v1 = 120 m.s-1

Therefore, the sedan car velocity relative to the ground is 120 m.s-1

Q. What is the meaning of an isolated system?

Ans: There must be two or more objects in order for a system to exist. For example, a system that is completely isolated from external influences is referred to as an isolated system.

A system that is isolated is one in which the only forces that contribute to the change in momentum of an individual item are the forces operating between the components themselves, and hence the object is not affected by any external forces.

There are two things that must happen for there to be a net external force:

  • There is an external force present in the system that originates from a source other than the two objects of the system.
  • A force that is unbalanced in relation to other forces.

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