Although I don't have any problems with vectors when using them in Mathematics but I am having a hard time using them in physics. It is really frustrating me.
Can you please recommend me some good resources for learning how to use vectors in physics?
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$\begingroup$ Perhaps "A Student's Guide to Vectors and Tensors" by Daniel Fleisch. $\endgroup$– HunterCommented May 21, 2014 at 11:46
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$\begingroup$ @Hunter Would you recommend it to a high school student? $\endgroup$– Shaurya GuptaCommented May 21, 2014 at 11:50
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$\begingroup$ Hmmm, I would recommend it to a first year university student, but I'm not sure if it appropriate for secondary school (it might be too advanced). Perhaps you can give us an example of your difficulties with vectors so that we can better help you. $\endgroup$– HunterCommented May 21, 2014 at 11:56
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$\begingroup$ @Hunter The things that trouble me are: 1. Choosing the right axes to solve problems efficiently. 2. Resolving vectors in a particular direction. e.g. If I stand on the $A$ of $\triangle ABC$ and my velocity is towards B, then what is the component towards the centroid? $\endgroup$– Shaurya GuptaCommented May 21, 2014 at 12:01
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$\begingroup$ Vectors are a tool used to describe models (cause and effect) in physics. I use vectors all the time in rigid body mechanics. What kind of problems are you looking to solve? $\endgroup$– John AlexiouCommented May 21, 2014 at 15:16
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1 Answer
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Fundamentals of Physics 8th Ed by Halliday, Resnick and Walker has a chapter exclusively on vector quantities (titled Vector Quantities) and is a good place to start. It clearly illustrates how one can use vectors to solve problems in physics, especially mechanics (essentially, what you are looking for). However, to gain a complete understanding, it is absolutely essential to solve the exercises given in the end.
The topics covered are:
- What is Physics?
- Vectors and Scalars
- Adding Vectors Geometrically
- Components of
- Vectors Unit Vectors
- Adding Vectors by Components
- Vectors and the Laws of Physics
- Multiplying Vectors
- Questions/Problem
This is sufficient for high school physics. And keep in mind, it is absolutely essential to solve the problems.
Now once you have mastered the basics and wish to study further, you may have to look elsewhere. There are plenty of textbooks on Mathematical Physics or Mathematical Methods available in the market that covers all the mathematics that is usually needed by an undergraduate student to do physics which includes vector analysis and vector calculus. I personally prefer 'Mathematical Methods for Physicists 7th Ed. ' by Arfken, Weber and Harris.
If you are already very familiar with vector algebra, this is a good place to start learning vector calculus. The strength lies in some of the illustrated examples and the exercises are also quite good. The topics covered are:
- Review of Basic Properties.
- Vectors in 3-D Space
- Coordinate Transformations
- Rotations in $R^3$
- Differential Vector Operators
- Differential Vector Operators: Further Properties
- Vector Integration
- Integral Theorems
- Potential Theory
- Curvilinear Coordinates
I hope this helps. Good luck!
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$\begingroup$ These are some specific problems that trouble me: 1. Choosing the right axes to solve problems efficiently. 2. Resolving vectors in a particular direction. e.g. If I stand on the A of equilateral △ABC and my velocity is towards B, then what is the component towards the centroid? $\endgroup$ Commented May 22, 2014 at 5:59
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$\begingroup$ Carefully reading Resnick Halliday and going through solved examples and finally solving problems on your own is the only way. $\endgroup$– noir1993Commented May 22, 2014 at 6:03
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$\begingroup$ That means if I carefully read the book(which I was already going to buy today), I won't have trouble with such problems? $\endgroup$ Commented May 22, 2014 at 6:04
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$\begingroup$ That is a very difficult question to answer. The book is a very popular one and I personally recommend it. It would be wise to download the ebook and go through it buying to see if you are comfortable with it. $\endgroup$– noir1993Commented May 22, 2014 at 6:07
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1$\begingroup$ See, what you are actually doing is taking the projection of the vector along the line joining a vertex to the center. Think along this line and you shall find the answer. $\endgroup$– noir1993Commented May 22, 2014 at 6:35