Law of Conservation of Momentum | XI PHY AKUEB (New Syllabus) | 2025-26

**Video Title:** 3.2 c) Law of Conservation of Momentum | XI PHY AKUEB (New Syllabus) | 2025-26 | (Urdu/Hindi)

**Channel:** Khan Affan

**Syllabus:** AKUEB Physics Class 11 (New Syllabus 2025-26)

**Language:** Urdu/Hindi (Explanation), English (Notes)

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1. Summary

This video lecture by Khan Affan explains the **Law of Conservation of Momentum** for Class 11 Physics, aligning with the AKUEB syllabus. It delves into the definition of momentum, the conditions under which momentum is conserved, and illustrates the concept with examples, particularly focusing on collisions between two bodies. The importance of this law in various physical scenarios is highlighted.

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2. Key Takeaways

* **Momentum (p)** is defined as the product of mass (m) and velocity (v): `p = mv`. It is a vector quantity.

* The **Law of Conservation of Momentum** states that in an isolated system (where no external forces act), the total momentum of the system remains constant.

* For a system of two interacting bodies, the total momentum *before* an interaction (like a collision) is equal to the total momentum *after* the interaction.

* Mathematically, for two bodies `1` and `2`: `m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂`, where `u` represents initial velocities and `v` represents final velocities.

* This law is a direct consequence of **Newton's Third Law of Motion** (Action-Reaction).

* The concept of conservation of momentum is applicable to various phenomena, including collisions (elastic and inelastic), explosions, and rocket propulsion.

* The absence of *external* forces is crucial for momentum conservation. Internal forces within the system (like forces during collision) do not change the total momentum.

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3. Detailed Notes

3.1. Definition of Momentum

* **Momentum (p)**: A measure of the quantity of motion an object possesses.

* Formula: `p = mv`

* Where:

* `p` = Momentum

* `m` = Mass of the object

* `v` = Velocity of the object

* **Nature**: Momentum is a **vector** quantity, meaning it has both magnitude and direction. The direction of momentum is the same as the direction of velocity.

3.2. Law of Conservation of Momentum

* **Statement**: "If no external force acts on a system, the total momentum of the system remains constant."

* **Conditions for Conservation**:

* The system must be **isolated**.

* An isolated system is one where the **net external force** acting on it is zero.

* Internal forces (forces between the objects within the system) do not affect the total momentum of the system. They can change the momentum of individual objects but not the sum.

* **Mathematical Representation (for a system of two bodies)**:

* Consider two bodies, Body 1 (mass `m₁`) and Body 2 (mass `m₂`).

* Let their initial velocities be `u₁` and `u₂` respectively.

* Let their final velocities after interaction be `v₁` and `v₂` respectively.

* According to the Law of Conservation of Momentum:

**Total Initial Momentum = Total Final Momentum**

`m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂`

3.3. Derivation from Newton's Laws

* The Law of Conservation of Momentum can be derived from Newton's Laws of Motion, particularly Newton's Third Law.

* **Newton's Third Law**: "For every action, there is an equal and opposite reaction."

* Consider a collision between two bodies A and B.

* Let `F_AB` be the force exerted by A on B.

* Let `F_BA` be the force exerted by B on A.

* According to Newton's Third Law: `F_AB = -F_BA`

* From Newton's Second Law, force is the rate of change of momentum: `F = dp/dt`.

* Therefore, `F_AB = dp_B/dt` and `F_BA = dp_A/dt`.

* Substituting these into the Third Law equation:

`dp_B/dt = -dp_A/dt`

`dp_B/dt + dp_A/dt = 0`

`(dp_A + dp_B)/dt = 0`

* This implies that the total change in momentum (`dp_A + dp_B`) over time is zero.

* If the total change in momentum is zero, then the total momentum (`p_A + p_B`) is constant.

`p_A + p_B = constant`

`m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂`

3.4. Applications and Examples

* **Collisions**:

* **Elastic Collisions**: Kinetic energy is conserved. Momentum is always conserved.

* **Inelastic Collisions**: Kinetic energy is not conserved (some is lost as heat, sound, deformation). Momentum is always conserved.

* *Example*: Two billiard balls colliding.

* **Explosions**:

* When an object explodes, the fragments move apart. The total momentum of the fragments immediately after the explosion is equal to the momentum of the object just before the explosion (if it was initially at rest, the total momentum is zero, and the vector sum of the momenta of the fragments will also be zero).

* *Example*: A bomb exploding in mid-air.

* **Rocket Propulsion**:

* A rocket expels mass (hot gas) backward at high velocity. By conservation of momentum, the rocket moves forward.

* **Recoil of a Gun**:

* When a bullet is fired from a gun, the gun recoils backward. The forward momentum of the bullet is balanced by the backward momentum of the gun.

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This structured note provides a comprehensive overview of the Law of Conservation of Momentum as presented in the video, suitable for AKUEB Class 11 Physics students.