Lesson 6 – Centre of Mass & System of Particles
Stage 1 : Concept of Centre of Mass
(Intermediate Physics – Complete Notes | Page 1)
In physics, many objects around us are not single particles. They are made up of a very large number of particles. Studying the motion of each particle separately is very difficult. To overcome this difficulty, physicists introduced the concept of Centre of Mass.
The centre of mass of a system is a point which represents the average position of the total mass of the system. The motion of the entire system can be studied by studying the motion of this single point.
Need for the Concept of Centre of Mass
Consider a moving train. The train is made up of many parts such as engine, coaches, passengers and luggage. It is not practical to describe the motion of each part separately. Instead, we treat the entire train as a single particle located at its centre of mass.
Thus, the centre of mass simplifies the study of motion of complex systems.
- Reduces a system of many particles to a single point
- Makes application of Newton’s laws easier
- Helps in understanding motion of rigid bodies
Definition of Centre of Mass
The centre of mass of a system of particles is defined as the point where the entire mass of the system can be considered to be concentrated for the purpose of studying translational motion.
Definition (Exam Ready):
The centre of mass is a point which describes the average position
of the total mass of a system of particles.
Important Properties of Centre of Mass
- The centre of mass may lie inside or outside the body
- Its position depends on mass distribution
- It is a mathematical point, not a physical particle
- For symmetric bodies, it lies at the geometric centre
Centre of Mass of Some Common Bodies
- Uniform rod – at its midpoint
- Uniform square or rectangle – at its centre
- Uniform circular ring – at the centre of the ring
- Uniform solid sphere – at its centre
These results are due to uniform mass distribution and symmetry.
Centre of Mass and Motion
When a body is in motion, all its particles move. However, the motion of the body as a whole can be described by the motion of its centre of mass.
If no external force acts on the system, the centre of mass moves with constant velocity or remains at rest.
Centre of Mass vs Centre of Gravity
Students often confuse centre of mass with centre of gravity. Though they may coincide in many cases, they are not always the same.
- Centre of Mass: depends only on mass distribution
- Centre of Gravity: depends on gravitational field
Near the Earth’s surface, the gravitational field is nearly uniform. Hence, centre of mass and centre of gravity coincide.
Intermediate Exam Orientation
From this topic, Intermediate examinations generally ask:
- Definition of centre of mass
- Difference between centre of mass and centre of gravity
- Centre of mass of simple bodies
- Conceptual explanation questions
Key Points to Remember
✔ Centre of mass represents the motion of the entire system
✔ It depends only on mass distribution
✔ It is a powerful concept used throughout mechanics
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