First of all, you're obviously not a university student, and state you want to become an astrophysicist. Then state that you don't want to be studying "stars and junk" - So what I can conclude from this is that you're naive about the area that you want to pursue.
There's many reasons for why I enjoy mathematics. One of my main reasons is the way to describe such a large variety of things using mathematics in very simple ways. For example in Linear Algebra, you can talk about many specific and different things such as vector spaces, and different types of...
Force is a change in momentum, the momentum changes for the first 3s and the last 2s - The force is constant since the decrease in velocity is linear. Find the change in velocity over the period of time when you know the momentum is changing, then you get the force. You know this is exact since...
It'd take you probably a 6 -12 months depending on your study habit. You'll need Linear Algebra, much more calculus and differential equations for much more advanced physics. For the Olympiad you need maximum the maths you have now.
Olympiad is for people who are interested in spending countless hours on the same questions for months and months. You can't do advanced books yet, you don't have the maths - You would need linear algebra and much more calculus than just single-variable.
Yes. Because practicing olympiad questions for hours and hours a week means you're the best at physics.
@Thread - Why do you want to go to CalTech/MIT? Do you actually want to do a PhD/research or do you want to do the same undergraduate courses that every university does but for 50 grand a year?
Simplifying my text, I'm trying to get the message across that you do what you want to do. If you don't want to do physics don't do it, simple as that.
I think lagrangian mechanics is better to do first then basic quantum mechanics, just some universities don't do it that way. It all depends on what you want to learn, I'm learning everything how I want to learn it because I think it's the best way. If you want to do the maths you've stated...
Momentum is just a property of a system, it basically arises from inertia. Momentum is just as if you threw a ball in outer space (far away from any other objects) by applying a force to it. So, let's consider the system of the ball and you (ball-you), the original state of the system is you and...
I don't know what you mean by reading 'Einstein's original paper'? Okay sure, you make a really stupid mistake by being careless of what you're reading. Does that imply that the information in the book isn't good enough for your standards?
Sure, you need to ask a few questions you're curious...