How to derive the 4 laws of motion using Calculus?

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Discussion Overview

The discussion revolves around the derivation of the laws of motion using calculus, with participants exploring the relationship between physical laws and mathematical frameworks. The scope includes theoretical considerations and the application of calculus to classical mechanics.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions how to derive the laws of motion using calculus from scratch.
  • Another participant argues that the laws of motion are physical laws that cannot be derived purely through calculus, emphasizing their basis in observation and experiment.
  • A different participant notes the common understanding of Newton's laws, mentioning that the second law, F = ma, involves calculus through the derivative of velocity with respect to time.
  • Another participant expresses confusion regarding the mention of four laws, suggesting that the work-energy theorem and angular momentum theorem are derived from the second law of motion.

Areas of Agreement / Disagreement

Participants express differing views on whether the laws of motion can be derived using calculus, with some asserting that they are fundamentally observational and others attempting to connect them to calculus through specific examples.

Contextual Notes

There is ambiguity regarding the reference to "four laws," as traditionally, there are three Newton's laws of motion. The discussion also highlights the dependence on definitions and interpretations of physical laws versus mathematical derivations.

MrDarkness
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How do you derive the laws of motion using Calculus from scratch
 
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You can't. The laws of motion are physical laws, independent of the foundations of mathematics. The laws can be stated in mathematical form and developed using mathematics, such as calculus.

But, they have to be postulated through observation and experiment.
 
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First of all, I thought there were 3 Newton's laws of motion.

Second of all (ironically speaking), the Newton's 2nd law states that F = ma. We can say that a is equivalent to the derivative of velocity wrt time. The derivative, in this case, uses calculus.
 
I do not understand which 4 laws are supposed to derive but the work energy theorem is usually derived from the 2nd Newton; as well as the angular momentum theorem is also a theorem and it is derived.
 

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