How Newton approximated force as change of momentum?

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Newton defined force as the change in momentum over time, emphasizing its role in understanding motion and interactions between objects. The discussion highlights the importance of mathematical relationships in physics, suggesting that equations provide clearer insights than lengthy explanations. Calculus, developed by Newton, is essential for describing variations and understanding concepts like force and momentum. The concept of force is framed as a means to express momentum conservation and the interactions between objects, with equal and opposite forces acting between them. Ultimately, grasping these relationships through mathematical definitions enhances the understanding of physical concepts.
joseph_seb
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why Newton had taken force as change in momentum per time?
i mean i need to get physical interpretation?what is this force actually?
also help me to get an idea about energy in sense(core concept)?
not with some equations?
i see these equations every time?but didn't know meanining?
somebody please help with these or give the name of texts which i should refer to?
 
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If you are going to get a good grasp of Physics then you will have to, at some point, start to see the mathematical relationships between quaitities as the best way of describing what goes on. An equation (particularly a simple one) states what happens so much better than a long sentence involving instances and examples.
If you look at Wiki (or all over the Web, in fact) for statements about Newton's Laws then they always end up with a bit of Maths. Just do a search and read as many links as you can.

(A form of) Calculus was invented by Newton in order to discuss the way that things vary in a concise way and differential Calculus describes so many processes very well. The "physical interpretation" that you seek may not always be there for some, even elementary relationships. If you are in a position to get hold of the elements of Maths and Calculus then you would find that approach very useful. The 'feeling' for Physics tends to follow the Maths, rather than the other way round.
 
Instead of asking what force is, consider what force is used for. The sum of forces is the change in momentum over time. That's not an approximation. The concept of force let's us express the conservation of momentum in another way. It's useful for decomposing the change in momentum of an object into the sum of contributions coming from other objects. Between each pair of objects, you have an equal and opposite force between them. As such, force represents a transfer of momentum between two objects.
 
It's a case of choosing your definitions so as to best capture your intuitive notion of "force" or whatever you want to describe. In the end all you can deal with is the relationships between the quantities you have defined, and there may be other similar definitions which capture other aspects of the intuitive notions you have in mind.
 
@sophiecentaur
you said, Calculus was invented by Newton in order to discuss the way that things vary in a concise way,ie,if it is integral calculus,it is the summation of continuous values represented by function,ie we it has a meaning;i'd like to get a simliar kinda explanation,ie,how the eqn f=dp/dt states what happens so much better than a long sentence involving instances and examples;ie,if u were the one to formulate this eqn, what is ur logic
 
@Khashishi
then what is momentum?
 

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