Lesson 6 – Centre of Mass & System of Particles

Stage 1: Concept of Centre of Mass

In mechanics, when a body consists of many particles, it becomes difficult to describe the motion of each particle separately. To simplify the analysis, we introduce a very powerful concept called Centre of Mass (COM).

The centre of mass of a system is a point that represents the average position of the entire mass of the system. The motion of this point tells us how the system behaves as a whole.

Why Do We Need Centre of Mass?

• Real bodies are made of many particles
• Tracking each particle is impossible
• Centre of mass reduces a complex system to a single point
• Newton’s laws can be applied to this single point

Important idea:
The entire system behaves as if all its mass were concentrated at the centre of mass.

Everyday Examples

• A moving bus behaves like a single particle located at its COM
• A jumping athlete controls body balance using COM
• In long jump, the athlete’s COM follows a parabolic path

Centre of Mass vs Centre of Gravity

Many students confuse these two terms.

• Centre of Mass: depends only on mass distribution
• Centre of Gravity: depends on gravitational field

In a uniform gravitational field (near Earth’s surface), centre of mass and centre of gravity coincide.

Exam-Oriented Note

In Intermediate exams, questions focus on:

• Definition of centre of mass
• Difference between COM and centre of gravity
• Simple physical understanding

In IIT-JEE, questions focus on:

• Motion of centre of mass
• COM of systems in motion
• Use of COM to simplify difficult problems

Key Takeaway (Must Remember)

The centre of mass is not always inside the body. It is a mathematical point that represents the system’s motion.

📘 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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Prepared by: Shaktimatha Learning 🌱
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