Lesson 6 – Centre of Mass & System of Particles

FINAL REVISION · PART–2
Formulas, Traps & One-Look Checks

This part is for fast revision. If you remember everything here, you are safe in both Board & IIT-JEE.

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1️⃣ Core Formulas (Do NOT Memorise Blindly)

Position of Centre of Mass:

r_cm = ( Σ m_i r_i ) / ( Σ m_i )

Velocity of Centre of Mass:

v_cm = ( Σ m_i v_i ) / M

Momentum of System:

P = M v_cm

These formulas work only when the system is correctly chosen.

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2️⃣ The Master Equation (Never Forget)

ΣF_external = M a_cm

✔ Valid for all systems
✔ Valid in inertial frames
✔ Internal forces are automatically cancelled

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3️⃣ Explosion & Fragmentation – One-Line Logic

Explosion = internal forces only ⇒ COM motion remains unchanged

✔ Path of COM does not bend
✔ Velocity of COM does not jump

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4️⃣ Frame-Based Questions – Quick Rule

Ask instantly:

“Is the observer accelerating?”

• If NO → inertial → apply COM law directly
• If YES → add pseudo force → then apply COM law

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5️⃣ Zero Momentum Trap (Very Common)

❌ Zero momentum ≠ zero acceleration

Acceleration depends on force, not on momentum value.

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6️⃣ Internal vs External Force – Instant Test

If the force comes from within the system boundary → internal → ignore for COM motion

Gravity, normal from ground, tension from support → usually external.

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7️⃣ Signs & Direction Check (1-Second Test)

Before final answer:

✔ Direction of force correct?
✔ Frame chosen correct?
✔ Does answer violate COM law?

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8️⃣ High-Frequency Exam Statements (Memorise)

• COM may lie outside the body
• Internal forces do not affect COM motion
• Acceleration of COM is same in all inertial frames
• Momentum conservation is a system property

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9️⃣ What NOT to Do in Exam

❌ Writing equations for each particle
❌ Doing algebra before law selection
❌ Panicking due to long question
❌ Mixing COM with energy unnecessarily

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🔟 Final 30-Second Mental Scan

✔ System identified
✔ External forces listed
✔ COM law applied
✔ Internal forces ignored
✔ Answer physically sensible

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✅ REVISION PART–2 CLOSURE

If you can recall this page calmly, you are exam-ready for COM.

Next comes Revision Part–3 — only 15 must-do questions with logic (no repetition).

📘 Centre of Mass & System of Particles – Complete Physics Library

This library is a complete learning package for Intermediate + IIT JEE Physics covering Centre of Mass and System of Particles.

It includes theory, solved examples, objective questions, IIT-level problems, revision strategies, tricks, and exam-oriented guidance.

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📂 Stage 1: Intermediate Complete Notes (Concept Foundation)

1. Part 1
2. Part 2
3. Part 3
4. Part 4
5. Part 5
6. Part 6
7. Part 7
8. Part 8
9. Part 9
10. Part 10

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📂 Stage 2: Advanced Concepts & Applications

11. Part 11
12. Part 12
13. Part 13
14. Part 14
15. Part 15
16. Part 16
17. Part 17
18. Part 18
19. Part 19
20. Part 20

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📂 Stage 3: Objective Questions, Tough Problems & Revision

21. Part 21
22. Part 22
23. Part 23
24. Part 24
25. Part 25
26. Part 26
27. Part 27
28. Part 28
29. Part 29
30. Part 30
31. Part 31
32. Part 32
33. Part 33
34. Part 34
35. Part 35
36. Part 36
37. Part 37
38. Part 38
39. Part 39
40. Part 40
41. Part 41
42. Part 42
43. Part 43
44. Part 44
45. Part 45
46. Part 46
47. Part 47
48. Part 48
49. Part 49
50. Part 50
51. Part 51
52. Part 52
53. Part 53
54. Part 54
55. Part 55
56. Part 56
57. Part 57

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