Use of Calculus in Newtons Laws

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SUMMARY

The discussion centers on the use of calculus in Newton's laws of motion, particularly the differential forms of these laws. The differential form, represented as F = dp/dt, provides a more general application than the simpler F = ma, which only applies when mass remains constant. The equation F = d(mv)/dt = m(dv/dt) illustrates that the differential form accommodates varying mass scenarios, highlighting its superiority in generality for physical situations.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Basic knowledge of calculus, specifically differentiation
  • Familiarity with the concept of momentum (p = mv)
  • Awareness of scenarios involving variable mass systems
NEXT STEPS
  • Study the implications of variable mass in classical mechanics
  • Learn advanced calculus techniques related to differential equations
  • Explore applications of Newton's laws in real-world physics problems
  • Investigate the relationship between momentum and force in dynamic systems
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Physics students, educators, and professionals interested in the mathematical foundations of classical mechanics and the application of calculus in understanding motion and forces.

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Why do I see Newtons 3 laws (mostly 2 and 3) given using differentials (F=dp/dt etc...) when it is far simpler to use the basic form F=ma (and the same for the 3rd law), is there an advantage to the more complicated form?
 
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The differential form is the general law. F=ma only follows if the mass remains constant.

[itex]F=\frac{d(mv)}{dt}=m\frac{dv}{dt}[/itex]

However all physical situations do not have constant mass. So the differential form has the advantage of generality.
 
That makes sense, thank you.
 

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