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  1. Why do we study the scalars such as work and energy if we know how to solve daily classical mechanics problem with standard mathematics?

  2. My second query is about the main motive of defining linear momentum in classical mechanics?

EDIT

I think that I had not conveyed my problem properly in my non edited version of this question. So I edit this question in order for proper functioning of the question.

Well my main motive to ask this question was to ask about a fundamental problem which I think all the respected physicist would already be acquainted with it. When I was playing with my fidget spinner I was somewhat astonished by a common fact in physics. I know that a system always want to minimise its potential energy. Well potential energy is my favourite topic. I want to know that when a system rotates about a stationary axis then how it wants to minimise its potential energy? Please explain in great detail.

Please explain the beauty of expansion of time derivative of linear momentum as it contains the term $\frac{vdm}{dt}$. I can't motivate myself that how Newton knew that the net force acting on a particle would be directly proportional to rate of change of mass as it is not quite intuitive. So please explain in great detail.

I would say that please give answers to the edited version of this question as GiorgioP has already explained the non edited version of the question beautifully.

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  • $\begingroup$ The system wants to reach a stationary point of the action $S$: $$S=\int_{t_1}^{t_2} L \mathrm{d}t$$ This is called Hamilton's principle or principle of stationary action. In classical mechanics, $L=T-V$, where $T$ is the kinetic energy of the system and $V$ is the potential energy. $\endgroup$ – Botond Mar 26 '19 at 14:38
  • $\begingroup$ Hi Botond I am a 13 year old student who has just completed classical mechanics by hiring a book from my senior friend. I haven't read so much about Hamilton's principles. $\endgroup$ – user213933 Mar 26 '19 at 14:40
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    $\begingroup$ Probably a new question would have been better than editing so heavily the original question. $\endgroup$ – GiorgioP Mar 26 '19 at 19:00
  • $\begingroup$ Take into account that, in the case of isolated and conservative systems, Newtonian dynamics does not minimize the potential energy. While the system is moving, there is a continuous exchange between potential and kinetic energy. $\endgroup$ – GiorgioP Mar 26 '19 at 19:04
  • $\begingroup$ Hi GiorgioP I don't know why they have banned me to ask new questions but I think that my questions are acceptable! $\endgroup$ – user213933 Mar 27 '19 at 11:21
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Work, energy and linear momentum can be considered as derived quantities, in classical mechanics, leaving to force, position and velocity a central role. However, it turns out that energy (requiring work for its definition) and momentum, in some cases are conserved quantities: they do not change during the motion. This property makes these two concepts extremely useful for describing and understanding classical motions. Think for example the huge simplification conservation principles bring in the description of scattering experiements.

Moreover, it is a fact that at a more fundamental level, classical mechanics is only a macroscopic approximation of the more fundamental laws of Quantum Mechanics. But in QM some of the classic concepts like trajectory or force become ill-defined, while momentum and energy play a central role.

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