What should I study or read to learn physics in a very fundamental way?

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SUMMARY

The discussion centers on a 15-year-old student seeking to learn physics fundamentally, specifically understanding concepts like Newton's law of gravitation, F = GmM/r². The student has completed single-variable calculus and will study vectors and Serway's physics curriculum next year. Recommendations for books that provide detailed explanations and mathematical rigor, suitable for the student's current level, are sought. The featured thread "So You Want to be a Physicist" is suggested for further exploration.

PREREQUISITES
  • Single-variable calculus knowledge
  • Basic understanding of vectors
  • Familiarity with Newtonian physics concepts
  • Interest in mathematical explanations of physical laws
NEXT STEPS
  • Research "Understanding Physics" by D.C. Heath for foundational concepts
  • Explore "The Feynman Lectures on Physics" for intuitive explanations
  • Study "Conceptual Physics" by Paul Hewitt for a non-mathematical approach
  • Review the featured thread "So You Want to be a Physicist" for additional resources
USEFUL FOR

This discussion is beneficial for high school students, aspiring physicists, and anyone interested in grasping the fundamental principles of physics with a focus on mathematical reasoning.

Danny Han
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Hello I'm a 15year old boy living in Korea, and lived in the U.S. for a couple of years. I want to learn physics in a very fundamental(?) way, for example, knowing the reason why from Newton's law of gravitation F = GmM/r^2, F is proportion to the SQUARE of r (not cube or power of 4??)

Currently I studied single variable calculus, and by the next year, I'll have finished vectors and Serway or Haliday( I forgot the spelling) (it's in our school curriculum)

I saw my friends reading books by hawking and so on, but they seemed to lack a detailed explanation and math(although I'm not good at math).

To sum it up, I want a book that talks about the fundamentals of physics using my level of math.( oh and our school will learn Serway next year, so please don't suggest me such books)
 
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