Lesson 7 – Momentum & Collisions

Phase 1: IIT / JEE Solved Problems
Page 5 – Concept Wrap-Up & IIT Traps

This page consolidates all Phase-1 ideas, highlights frequent IIT/JEE mistakes, and prepares the student mentally for Phase-2 (Tough / Advanced problems).

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1️⃣ Core Concepts You Must Be Fluent With

✔ Linear momentum is always conserved in absence of external force
✔ Coefficient of restitution connects relative velocities
✔ Energy conservation applies only to elastic collisions
✔ Impulse = change in momentum
✔ Explosion problems always start with zero total momentum

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2️⃣ Quick IIT Concept Check (Self-Test)

• Can KE increase while momentum is conserved?
• When can we directly use e = separation / approach?
• Why is height after bounce proportional to e²?
• Why is recoil velocity of gun very small?

👉 If you can answer all clearly, you are Phase-2 ready.

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3️⃣ Common IIT/JEE Mistakes (Very Important)

❌ Mixing directions without sign convention
❌ Using KE conservation in inelastic collision
❌ Forgetting that wall has infinite mass
❌ Writing e = v₁ − v₂ / u₁ − u₂ without order
❌ Ignoring internal energy in explosions

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4️⃣ IIT Shortcuts & High-Speed Insights

✔ Equal masses + elastic → velocity exchange
✔ One body at rest → use relative velocity directly
✔ Vertical bounce → height ratio = e²
✔ Explosion → directions opposite automatically
✔ Fraction KE questions → avoid full algebra

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5️⃣ What Changes in Phase 2 (Tough Problems)?

In Phase 2, problems will involve:

• Multiple collisions
• Variable masses and frames
• Hidden constraints
• Conceptual elimination instead of full calculation

👉 Phase 2 tests thinking style, not formulas.

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📌 Phase-1 Final Note

✔ Phase-1 = Foundation + Confidence
✔ Every formula is now meaningful
✔ You are prepared to face IIT-level traps
✔ Next level demands patience and strategy

👉 Next: Phase 2 – IIT / JEE Tough Problems (Advanced Thinking)