B How to derive the 4 laws of motion using Calculus?

  • B
  • Thread starter Thread starter MrDarkness
  • Start date Start date
  • Tags Tags
    Newton equations
Click For Summary
The laws of motion cannot be derived purely from calculus, as they are fundamentally physical laws based on empirical observation and experimentation. While calculus can be used to express and develop these laws mathematically, their origins lie in physical principles rather than mathematical foundations. The formulation of these laws requires postulation based on real-world phenomena. Therefore, understanding the laws of motion involves both mathematical representation and physical experimentation. Ultimately, the relationship between calculus and the laws of motion is one of application rather than derivation.
MrDarkness
Messages
1
Reaction score
0
How do you derive the laws of motion using Calculus from scratch
 
Physics news on Phys.org
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.
 
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.
 
Thread 'Energy requirements of a 4 wheel drive boat'

Thread 'Energy requirements of a 4 wheel drive boat'

4 wheel drive amphibious boat (swamp buggy?) My problem is trying to calculate the amount of energy, or a good estimate, that would be required to keep the boat levitated above the water at the approximate water line shown in the second drawing. I don’t believe it will require as much energy as a helicopter as the blades are pushing against a semi-solid surface but I really don’t know? A planing hull has a lift / drag ratio of about 5:1 with skin friction becoming increasingly more...
View full post »

Similar threads

I Using reference frames for derivation of Lagrangian
Replies
25
Views
3K
I Extending Newton's laws -- Is the concept of force still defined?
Replies
35
Views
5K
B Is Newton's first law of motion applicable when walking?
Replies
2
Views
2K
B Are frictional forces action forces or reaction forces?
Replies
14
Views
1K
Is Newton's Law of Gravity Still Accurate Despite Einstein's Discoveries?
Replies
4
Views
2K
I Newton's Third Law: Action & Reaction Along the Line Connecting Two Objects
Replies
5
Views
1K
Insights How to Apply Newton’s Second Law to Variable Mass Systems
Replies
0
Views
2K
B Proof of inverse square law for gravitation?
Replies
18
Views
2K
Understanding Newton's First Law and Referential Inertial on a Moving Earth
Replies
1
Views
1K
B Newton’s second law as one complete law
Replies
27
Views
2K