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Well, to get your theory right and building the foundations I used University Physics by Zeemansky, Young and Sears. Since you seem from India- I also used the DC Pandey books ( but only for exam oriented purposes like IIT and Jee Mains- NOT suitable as textbooks) And if you truly want to solve problems I.E.Irodov's Problems in General Physics is the best book out there. But, it only has problems, and mighty conceptual ones at that. But, it is awesome to solve from here.
Thanks; though to make it up for Irodov's problem what does it take?
I went to the MIT page for the Classical Mechanics I course. The book they suggest is "Sears and Zemansky's University Physics: with Modern Physics. 12th edition." That book will be most compatible with this course and since it is suggested by MIT, I'm sure it's quite reliable. Hope this helped:)
Firstly, you'd need to be strong conceptually. You need to VISUALISE the problems. (This is the key for any Physics problem, especially in Mechanics). Like, trying to think what is going to happen and how. Then you need to know basic calculus, integration and differentiation. Know the formulas and their applications well. (D.C.Pandey helps here). Well, that's about it. Although, I should tell you that Irodov is mainly intended for college level. So, you won't be able to do all the problems. And it is not required for the entrance exams. But do solve it if you're enjoy Physics. At first you might face difficulty in solving easy problems, but once you get the hang of the book and realise how conceptual it is, it becomes insanely fun. :)
Halliday's book or Feynman's Lecture on Physics
okay, but Feynmans LP doesn't quite help out for grades!
Halliday's Principle of Physics 9th edition clearly demonstrates why we need certain equations. It has concrete definitions and good questions.(Although I highly recommend that you do not try to solve all the questions; there are so many of them!) Serway's College Physics 9th edition has clear explanation. It's easy to read.