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When two or more bodies are acting upon each other, the complete momentum is said to be constant unless an external force is applied. This is known as the law of conservation of linear momentum.
So, the momentum can neither be created nor destroyed. In other words, between the two objects, the total momentum which takes place before the collision is equal to the total momentum which takes place after the collision. Total momentum tends to be conserved which means it is constant or doesn’t change. Further, we will understand about the law of conservation of linear momentum and its applications.
Logic behind the law of conservation of momentum:
Let us assume that the collision is happening between two objects, object A and object B. In such a collision, the forces which are acting between the objects have equal magnitude but they are acting in the opposite direction, which is actually Newton’s third law.
These forces act for a certain period of time, sometimes the time can be long and sometimes it can be short, but irrespective of how long or short the time is, it is said that the time which is acting upon object 1 is equal to the time acting upon object 2.
With the above statements, it is clear that the forces acting are equal in magnitude and opposite in direction and the times on which they are acting are equal in magnitude. It means that the impulses which are experienced by two objects are also equal in magnitude and opposite in direction.
But, the impulse which is experienced by an object tends to be equal to the change in momentum of that object; this is the impulse momentum change theorem. Logically, if each object experiences equal and opposite impulse, it will also experience equal and opposite momentum.
m1*Δv1 = -m2*Δv2
Let us understand the law of conservation of momentum using a real life analogy. This involves money transactions between two people – say there are two friends John and Seema. John has $100 and even Seema has $100, the total amount of money before any transaction taking place is $200. John gives 50$ to Seema. Now, Seema has 150$ and John has 50$, but the total amount even after the transaction is 200$, which means the money before and after transaction remains constant.
Law of conservation of momentum and its applications:
- Launching of rockets: We all are fascinated by the concept of rocket launches, but the whole process takes place because of the law of conservation of momentum. When a rocket is launched, the fuel which is burning is ejected at the lower end of the rocket and will move in the opposite direction, the rocket mass keeps on decreasing along the burning fuel, due to which the momentum of the rocket goes on increasing. Hence, the total momentum of the entire system which includes the rocket and fuel will remain the same like it was before the repulsion of the rocket.
- Recoiling of the gun: According to Newton’s third law, every action tends to have an equal and opposite reaction. So, when firing of the bullet takes place, a backward force acts upon the gun, the total momentum of the bullet and the gun which is recoiled remains zero.
- Air balloons: The air inside and the balloon together form a system, the balloon will be at rest initially and when it is set free, the air rushes out in the opposite direction. It possesses momentum. This is an example of law of conservation of momentum.
- Motor boats: The water is pushed backward and it gets pushed forward as a reaction to conserve momentum.
Differences between Torque and Angular Momentum
Now that we have understood the linear momentum, let’s examine the differences between conservation of linear momentum and Angular Momentum. The below table shows the differences between linear momentum and angular momentum:
Basis of differentiation | linear momentum | Angular Momentum |
Definition | A vector quantity equal to the product of the mass and the velocity of the centre of mass. | Angular Momentum is the product of a rotating object’s moment of inertia and angular velocity |
Mathematical Formula | The product of an object’s mass (m) and velocity (v) is defined as linear momentum (v). When an object has more momentum, it is more difficult to stop it. Therefore, the formula for linear momentum is p = mv. | Angular Momentum = Iω Here, I is the object’s moment of Inertia and w is the angular velocity at which the object is rotating. |
Examples | 1. Recoiling of the gun : According to Newton’s third law, every action tends to have an equal and opposite reaction. So when firing of the bullet takes place, a backward force acts upon the gun, the total momentum of the bullet and the gun which is recoiled remains zero.
| 1. When a skater spins her body on the ice turf, it is the angular momentum that prevents her from falling down. 2. The angular momentum prevents the merry-go-round from losing its balance. The same can be said about a giant-wheel as well. |
Conclusion
Linear momentum is a concept in Physics that determines the product of the mass and velocity of a particle. It evaluates the force of each particle and analyses the impact of each particle. Students must understand the concept of mass and speed before understanding linear momentum. This way, they will understand the properties of linear momentum of a system of particles. Applying the law of conservation of momentum is also important because it helps prevent collision problems. It also analyses the system of particles moving faster.
