Law of Conservation of Linear Momentum

In physics, the law of conservation of linear momentum states that within a closed system, the total linear momentum remains constant unless acted upon by an external force. This fundamental principle of the laws of physics implies that the total momentum of all objects within an isolated system, where no external forces are at play, will not change over time.

What is Law of Conservation of Linear Momentum?

Law of Conservation of Linear Momentum Formula

The Law of Conservation of Linear Momentum can be expressed using the formula:

• 𝑚₁​ and 𝑚₂ are the masses of two objects.
• 𝑣₁ᵢ​ and 𝑣₂ᵢ are the initial velocities of the two objects.
• 𝑣₁բ and 𝑣₂բ​ are the final velocities of the two objects.

This formula shows that the total linear momentum before an interaction (left side of the equation) is equal to the total linear momentum after the interaction (right side of the equation). Provided no external forces act on the system.

Law of Conservation of Linear Momentum Derivation

Here’s a simplified derivation of the Law of Conservation of Linear Momentum:

Initial State: Consider two objects moving in an isolated system, which means there are no external forces acting on them. Each object has its own momentum based on its mass and velocity.

Interaction: When these objects interact (collide or push against each other), they exert equal and opposite forces on one another, as per Newton’s Third Law.

Change in Momentum: Due to the interaction, each object’s momentum will change. One object might speed up, slow down, or change direction, and the same will happen for the other object, but in an opposite way.

Final State: After the interaction, the total momentum of the system remains the same as it was before the interaction. The changes in momentum of the individual objects cancel each other out. Meaning that the sum of their momenta remains unchanged.

The Law of Conservation of Linear Momentum tells us that as long as no external forces are acting on a system, the total momentum of the system remains constant. Even though the individual momenta of the objects within the system may change due to their interactions.

Uses of Law of Conservation of Linear Momentum

• Collision Analysis: Understanding interactions between vehicles, sports equipment, or particles.
• Rocket Propulsion: Explaining how rockets and jet engines generate thrust.
• Explosions and Recoil: Analyzing the movement of fragments and firearms after firing.
• Astronomy and Space: Studying celestial object interactions and orbital dynamics.
• Sports Physics: Investigating the motion of balls, players, and equipment.
• Quantum Mechanics: Understanding particle interactions and reactions.
• Engineering and Robotics: Designing systems with controlled motion and stability.

Examples for Law of Conservation of Linear Momentum

1. Billiards Game: When a cue ball strikes another ball on the billiard table, the total momentum of both balls before and after the collision remains constant, assuming no external forces like friction are significant.
2. Recoil of a Gun: When a gun is fired, the bullet moves forward while the gun recoils backward. The forward momentum of the bullet is balanced by the backward momentum of the gun, maintaining the total momentum of the system.
3. Rocket Launch: In space, a rocket expels gas backward at high speed, which generates thrust and pushes the rocket forward. Conserving the total momentum of the rocket and its exhaust gases.
4. Car Crash: During a car collision, the total momentum of both vehicles before and after the crash remains the same, assuming no external forces act on the system.
5. Skater’s Push: When two skaters push off each other on ice. They move in opposite directions. The total momentum of both skaters before and after the push remains the same.
6. Exploding Firecracker: When a firecracker explodes the total momentum of all the fragments flying in different directions. Equals the momentum of the firecracker before the explosion.

FAQ’S

What is the law of conservation of linear momentum investigation?

An investigation tests this law by analyzing collisions or interactions, checking if the total momentum before and after remains constant when no external forces act.

What is the conservation of linear impulse and momentum?

This principle links impulse (force times time) to momentum change, implying that momentum changes based on external forces over time, but remains conserved in isolated systems.

What is the SI unit of momentum?

In physics, the momentum of an object, a product of its mass and velocity, is measured in kilogram meters per second (kg·m/s).