1. What is a System of Particles?
A system of particles refers to a group of two or more particles considered together as a single unit for studying motion. Instead of analysing each particle individually, we examine the collective behaviour of the entire group. This approach helps simplify problems involving complex bodies, everyday objects, or natural systems.
For example, when we observe a car, a football, or even a rocket, we do not track every tiny piece inside them. We treat the whole object as one system whose collective motion can be described using basic principles.
1.1. Why We Group Particles Together
Real-world objects consist of countless atoms and molecules. Analysing each of them separately is impossible. To handle this, physics treats such objects as a system where only the overall behaviour matters. This makes calculations easier and helps us understand motion, forces, and energy without unnecessary complexity.
1.1.1. Examples from Daily Life
- A moving car treated as a single object, not millions of particles.
- A cricket ball considered as one unit even though it contains layers of cork, thread, and leather.
- A rocket whose motion is studied by analysing its entire mass, not its individual parts.
2. Internal and External Forces
Every particle inside a system experiences forces. Some forces come from other particles inside the system (internal forces), while others come from outside (external forces). Understanding this difference helps us predict how the system moves as a whole.
2.1. Internal Forces
These are forces that particles within the system exert on each other. For example, forces between atoms in a solid or between molecules in a fluid.
According to Newton’s Third Law, internal forces occur in equal and opposite pairs. Therefore, they cancel out when we examine the system as a whole.
2.2. External Forces
External forces originate from outside the system. Common examples include gravity, friction, tension, and applied pushes or pulls.
External forces decide how the entire system moves. If no external force acts, the system’s motion follows simple conservation laws.
3. Describing the Motion of a System
Even though the particles inside a system may move in different ways, we can still describe the motion of the entire system using a few key ideas. The most important of these are the centre of mass and total momentum.
3.1. Centre of Mass
The centre of mass (COM) is a special point where the whole mass of a system can be assumed to be concentrated. Its position is calculated using:
\( x_{cm} = \dfrac{m_1 x_1 + m_2 x_2 + \cdots}{m_1 + m_2 + \cdots} \)
In upcoming topics, we will learn how to calculate the centre of mass for different systems and bodies.
3.2. Total Momentum of the System
The total momentum of a system is the vector sum of momenta of all particles:
\( \vec{P} = \sum_i m_i \vec{v}_i \)
This helps us understand how the system moves when external forces act on it.
4. Why Treating a System as One Object Helps
Instead of tracking every particle, physics allows us to study the entire system through simpler quantities like centre of mass motion or total momentum. This reduces complex problems into manageable ones and forms the basis for understanding rotation, collision, explosion, and rigid body motion.
4.1. Simplifying Motion Analysis
Once we know how the centre of mass behaves, we can understand how the whole object moves—even if internal motion is complicated.
4.2. Useful in Real-World Applications
- Rocket motion and recoil
- Movement of vehicles
- Object rotation such as wheels and gears
- Studying collisions in physics and engineering