Lesson 7 – Momentum & Collisions

Stage 1: Intermediate Complete Notes
Page 3 – Conservation of Linear Momentum

The principle of conservation of linear momentum is one of the most powerful laws in Physics. It helps us analyze collisions, explosions, recoil, and many natural phenomena.

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1️⃣ Statement of Conservation of Linear Momentum

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

This law is valid for:

• Two-body systems
• Multi-particle systems
• Collisions and explosions

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2️⃣ Mathematical Expression

For a system of particles:

Total momentum before interaction = Total momentum after interaction

p_initial = p_final

This means:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

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3️⃣ Proof Using Newton’s Third Law

Consider two bodies interacting with each other.

According to Newton’s Third Law:

Force exerted by body 1 on body 2 = – Force exerted by body 2 on body 1

Using F = dp/dt:

d(p₁ + p₂)/dt = 0

Integrating with respect to time:

p₁ + p₂ = constant

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4️⃣ Conditions for Conservation of Momentum

✔ Net external force on the system must be zero
✔ Internal forces may act but cancel each other
✔ System must be isolated

External forces like friction, air resistance, or applied force can break momentum conservation.

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5️⃣ Real-Life Examples

• Recoil of a gun when a bullet is fired.
• Two skaters pushing each other and moving in opposite directions.
• Explosion of a bomb into fragments.

👉 In all these cases, total momentum before and after interaction remains constant.

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6️⃣ Momentum Conservation in One Dimension

In one-dimensional motion (straight line), vector nature of momentum reduces to sign (+ or –).

Choose one direction as positive and stick to it throughout the problem.

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7️⃣ Important Exam Notes

✔ Momentum conservation is independent of type of collision
✔ Valid even in inelastic collisions
✔ Always apply to the complete system

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📌 Page 3 Summary

✔ Momentum is conserved when net external force is zero
✔ Based on Newton’s Third Law
✔ Applicable to collisions and explosions
✔ Extremely important for board and IIT exams

👉 Next page: Types of Collisions – Elastic & Inelastic