In Newtonian mechanics, a particle (in my knowledge) is a point-like mass with no shape and size, deformation, rotation and internal movements, which is an idealized model of an object which does have shape and size and can have deformation, rotation and internal movements.
Newton's Laws of Motion (in my knowledge) are originally given for particles but can be extended for extended bodies, like for a rigid body.
To derive Newton's Second Law for a rigid body we can consider (as my textbook says) it to be a collection of particles.
I do not understand that when we say a rigid body is a system of particles, what are we referring to 'particles' here? Atoms? a differential element of the material? or something else?
As an extension of this question, can we consider a deformable body as a collection of particles and develop the Newton's Second Law for it as well? If yes then what will be the 'particle' in the case of deformable body?
Best Answer
TL;DR Never forget that we are talking about models here. We know that they cover only part of reality, but they are good enough and much easier to handle than "the full story".
A model need not correspond to each and every aspect of reality, only to those that we are interested in, that we need for our calculations. We want models that allow us to easily compute results that match reality to a degree that satisfies our needs.
So, if we talk about rigid bodies in Newtonian mechanics, we are interested in their movement and rotation as caused by external forces.
You mention the "wiggling of atoms" at the microscopic level (thermodynamics). You are absolutely correct. In an apple falling down from a tree, you don't have all atoms moving parallel, all with the same speed and direction, but instead each atom with its own chaotic movement.
We observed in many experiments that rigid macroscopic bodies react to forces the same way, regardless of their temperature (the amount of atom wiggling). So, a model of non-moving atoms in itself only represents absolute zero temperature, but we found out that it also matches our observations at higher temperatures. So, although we know that in reality we have a chaotic movement of particles, we can still use a model without that micro-level movement and get the correct result. This is an experiment-based justification for ignoring the "wiggling", but we can also do it mathematically.
If we take this chaotic micro-movement into account, we need to use statistics. And after some higher-mathematics calculations, we'll find out that, if we have enough atoms, the chaotic atom wiggling cancels itself out of all our formulas. The expected difference between the zero-temperature model and the wiggling-atoms model (as calculated based on a statistics model) quickly falls below any margin relevant for real life.