Lesson 6 – Centre of Mass & System of Particles

FINAL REVISION · PART–1
Concepts, Laws & Mental Framework

This revision part is meant to be read before attempting questions. If this part is clear, most COM problems become easy automatically.

---

1️⃣ What is a System of Particles?

A system of particles is a collection of two or more bodies whose motions may be interrelated.

Instead of tracking each particle separately, Physics allows us to describe the motion of the entire system using the concept of Centre of Mass (COM).

---

2️⃣ Definition of Centre of Mass

Centre of mass is the point at which the entire mass of a system can be assumed to be concentrated for the purpose of translational motion.

COM depends on mass distribution, not on shape or size.

---

3️⃣ Position of Centre of Mass (Concept)

For discrete particles:

r_cm = (m₁r₁ + m₂r₂ + ... ) / (m₁ + m₂ + ...)

The COM may:

• Lie inside the body
• Lie outside the body (ring, hollow sphere)
• Coincide with geometrical centre (uniform body)

---

4️⃣ The MOST IMPORTANT LAW (Heart of COM)

ΣF_external = M a_cm

This single equation governs the entire motion of the centre of mass.

👉 Internal forces NEVER appear in this equation.

---

5️⃣ Motion of Centre of Mass (Key Results)

• If net external force = 0 → COM moves with constant velocity
• If net external force ≠ 0 → COM accelerates
• COM acceleration depends ONLY on external force
• Internal forces do not affect COM motion

---

6️⃣ Momentum & Centre of Mass

Total momentum of a system:

P = M v_cm

Therefore:

• If momentum is conserved → COM velocity is constant
• Explosion, collision → internal → momentum conserved
• Momentum conservation is a COM concept

---

7️⃣ Explosion & Fragmentation (Very Important)

During an explosion:

• Forces involved are internal
• COM motion remains unchanged
• Path of COM is NOT altered

Explosion may change fragment motion, but NEVER the COM path.

---

8️⃣ Reference Frames & COM

In inertial frames:

• COM laws apply directly
• Acceleration of COM is frame-invariant

In non-inertial frames:

• Pseudo force must be added
• COM law still works after correction

---

9️⃣ Common Misconceptions (Must Remove)

❌ Zero momentum ≠ zero acceleration
❌ Internal force ≠ affects COM motion
❌ COM must lie inside body (false)
❌ Long question = difficult (false)

---

🔟 Mental Checklist Before Any COM Question

✔ Identify the system clearly
✔ List external forces only
✔ Apply ΣF = M a_cm
✔ Ignore internal complexity
✔ Stay calm — law is simple

---

✅ REVISION PART–1 CLOSURE

If this part is clear, 50–60% of COM problems can be answered without calculation.

Now the mind is ready for Revision Part–2 (Formulas + Traps + Quick Examples).

📘 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.

---

📂 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

---

📂 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

---

📂 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

---

🔗 Learning Hub & Community

• 📚 Shaktimatha Learning Resource Hub
• 📢 WhatsApp Learning Channel

---

Prepared by: Shaktimatha Learning 🌱
Vision: Concept clarity • Logical thinking • Exam excellence