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

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

---

1. Summary

This video lecture by Khan Affan explains the **Law of Conservation of Momentum** for Class 11 Physics, aligning with the AKUEB (Aga Khan University Examination Board) new syllabus for 2025-26. The video emphasizes that in the absence of external forces, the total momentum of an isolated system remains constant. It delves into the concept of momentum as a vector quantity and illustrates its conservation through examples, particularly focusing on collisions. The lecture aims to provide free conceptual physics education to students, especially those with limited resources.

---

2. Key Takeaways

* **Definition of Momentum:** Momentum (p) is the product of an object's mass (m) and its velocity (v) - **p = mv**. It is a vector quantity.

* **Law of Conservation of Momentum:** In an isolated system (where no net external force acts), the total momentum of the system remains constant.

* **Mathematical Representation:** For a system of two bodies, the total initial momentum is equal to the total final momentum: **m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂**, where 'u' represents initial velocity and 'v' represents final velocity.

* **Application in Collisions:** The law is particularly useful in analyzing collisions between objects.

* **Vector Nature:** Momentum conservation applies in all directions independently.

* **Isolated System:** The condition of an "isolated system" is crucial for the law to hold true. External forces can change the momentum of the system.

* **Conceptual Understanding:** The video aims to build a strong conceptual understanding of momentum and its conservation.

---

3. Detailed Notes

#### I. Introduction to Momentum

* **Definition:**

* Momentum is the "quantity of motion" an object possesses.

* Mathematically, momentum ($p$) = mass ($m$) × velocity ($v$).

* $p = mv$

* **Nature of Momentum:**

* Momentum is a **vector quantity**. It has both magnitude and direction.

* The direction of momentum is the same as the direction of velocity.

* **Units of Momentum:**

* SI unit: kilogram-meter per second (kg⋅m/s).

* Other units: Newton-second (N⋅s).

#### II. Newton's Second Law and Momentum

* **Relationship:** Newton's Second Law of Motion can be expressed in terms of momentum.

* **Force and Rate of Change of Momentum:** The net external force acting on an object is equal to the rate of change of its momentum.

* $F_{net} = \frac{\Delta p}{\Delta t}$

* $F_{net} = \frac{p_f - p_i}{\Delta t} = \frac{mv_f - mv_i}{\Delta t}$

#### III. Law of Conservation of Momentum

* **Statement:** If the net external force acting on a system is zero, then the total momentum of the system remains constant.

* "In the absence of external forces, the total momentum of an isolated system is conserved."

* **Isolated System:**

* An isolated system is one where no net external force acts upon it. Forces *within* the system (e.g., internal forces during a collision) are considered.

* **Mathematical Formulation:**

* Consider a system of two bodies (1 and 2) interacting with each other.

* Initial momentum of body 1: $p_{i1} = m_1u_1$

* Initial momentum of body 2: $p_{i2} = m_2u_2$

* Total initial momentum of the system: $P_i = p_{i1} + p_{i2} = m_1u_1 + m_2u_2$

* Final momentum of body 1: $p_{f1} = m_1v_1$

* Final momentum of body 2: $p_{f2} = m_2v_2$

* Total final momentum of the system: $P_f = p_{f1} + p_{f2} = m_1v_1 + m_2v_2$

* According to the law of conservation of momentum: $P_i = P_f$

* Therefore: **$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$**

* **Vector Nature:** This equation holds true in each direction (x, y, z) independently because momentum is a vector.

#### IV. Application of Conservation of Momentum

* **Collisions:**

* The law is fundamental to understanding collisions. During a collision, the forces between the colliding objects are internal forces.

* **Example:** Consider two billiard balls colliding. The force exerted by ball A on ball B is equal and opposite to the force exerted by ball B on ball A (Newton's Third Law). These are internal forces. If there's no external friction or air resistance, the total momentum of the two-ball system just before the collision is equal to the total momentum just after the collision.

* **Explosions/Recoil:**

* When an object explodes or recoils (like a gun firing), the total momentum before the event is zero (if initially at rest). After the explosion/recoil, the momenta of the fragments or the projectile and gun will sum up to zero, meaning they move in opposite directions with equal and opposite momentum.

#### V. Importance and Conceptual Understanding

* **Fundamental Principle:** The Law of Conservation of Momentum is one of the most fundamental principles in physics.

* **Problem Solving:** It provides a powerful tool for solving problems involving interactions between objects, especially when forces are difficult to calculate directly.

* **Conceptual Clarity:** The video aims to ensure students grasp the underlying concepts rather than just memorizing formulas.

---

**Note:** The lecture is delivered in Urdu/Hindi, with written explanations in English, catering to a diverse student audience. The content is aligned with the AKUEB syllabus for Class 11 Physics for the academic year 2025-26.