# I rewrote the Friction chapter from Tipler & Mosca

• walking
In summary, the conversation discusses a new note-taking method developed to filter out irrelevant information and improve clarity. The method was applied to the friction chapter in the Tipler and Mosca textbook, with the proposition that friction is independent of surface area being proven. The chapter also covers three types of friction (static, kinetic, and rolling) and their corresponding formulas, as well as drag forces between an object and a fluid. The conversation also mentions potential benefits of sharing the note-taking and reading method.
walking
I am testing a new note-taking method which I invented recently in order to help filter out irrelevant information and focus on what is actually useful and worth noting down/remembering. I then applied this to the Friction chapter in the tipler/mosca textbook as a way of testing out how this method allows clarity. I am simply sharing this in order to get feedback on whether it is clearer than the original textbook exposition of friction, and whether people would find it useful if I continue doing this for the rest of the book as I continue studying it. I am also willing to share the note-taking and reading method which I developed if anyone is interested.

Rewritten friction chapter of Tipler & Mosca:

1. An opposing force is a force which opposes relative motion between two surfaces.

2. There are two types of opposing forces: frictional and drag.

3. Friction is an electromagnetic attractive force which opposes the relative motion of two objects in sufficiently close contact.

4. Our first proposition regarding friction is that it is independent of the surface area of the objects in contact.

5. The argument for this is as follows. At the microscopic level, two objects only actually contact at widely spaced prominances called asperities. As the friction and hence the em attraction between the objects increases, the asperities are more squashed together increasing the microscopic contact area, thus friction is proportional to microscopic contact area. Having established this, we observe that when an object lying on a side of greater surface area is switched to a side of lesser surface area, the microscopic contact area decreases while the force at each asperity increases due to the greater force per unit area, creating greater squashing. These two effects cancel each other out and the result is that the microscopic contact area remains unchanged, and hence also the friction is unchanged since as we showed already, friction is proportional to microscopic contact area. This proves the proposition.

6. Now there are three types of friction:
-Static friction
-Kinetic friction
-Rolling friction

7. Static friction is the friction which occurs between two objects at rest relative to each other.

8. The mathematical description of static friction is ##f_s\le \mu_s F_n## where ##\mu_s## is a constant called the coefficient of static friction and depends on the nature of the surfaces in contact, and ##F_n## is the normal contact force.

9. It is actually found that frictional forces are generally of the form ##f=\mu F_n##. The argument for this is that as friction and hence em forces between two surfaces increase, the surfaces must be pushing each other with more force, meaning that the normal contact force between them is also higher. Thus, friction is proportional to normal contact force, and he constant of proportionality, ##\mu##, is simply found by experiment for each particular kind of surface.

10. An interesting result regarding static friction is that the angle at which maximum static friction occurs is given by ##tan \theta = \mu_s##. The argument for this doesn't contain anything new and can be easily proved using the previous results and basic dynamics.

11. Kinetic friction is the friction between two objects in relative, sliding motion.

12. The formula for it is ##f_k=\mu_k F_n##.

13. Kinetic friction is less than maximum static friction.

14. Rolling friction is the friction between two objects in relative, rolling motion, such as when a wheel rolls along the ground.

15. The formula for it is ##f_r=\mu_r F_n##.

16. A good example of the three types of friction is a car wheel. The accelerating force of a car wheel at low speed is static friction. At higher speeds this becomes kinetic friction. Alongside either of these, there is also rolling friction opposing the direction of the car's motion.

17. The explanation for these is as follows. Static friction is because the wheel tries to slide backwards and this relative motion is opposed by the ground, keeping the wheel static relative to the ground. At higher speeds however, the wheel actually slides and so the accelerating force becomes kinetic friction instead. Finally, rolling friction occurs throughout because the wheel is always peeling away from the ground, and the em attraction opposes this relative motion between wheel and ground, thus causing a friction opposing the wheel's tendency to peel forwards.

18. We now come to drag forces, which are forces between an object and a fluid, rather than two objects. (A "fluid" is simply any liquid or gas, such as water or air.)

19. The formula for drag forces is ##f=bv^n##, where b is a constant depending on factors such as the shape of the object, with objects of greater surface area having a higher value of b.

20. A parachute is an application of this to reduce the terminal speed of a skydiver.

21. The mathematics of this is that as skydiver falls at terminal speed, their weight and drag force are equal. Then as the parachute opens, the drag force increases and thus becomes greater than the weight. This causes the skydiver to accelerate upwards, thus reducing their speed. As the speed reduces, ##bv^n## reduces until it again becomes equal to the weight, but now at a new, lower terminal speed. This low terminal speed continues until the diver reaches the ground.

I have omitted a few parts such as the thresh-hold breaking system which was described in this chapter. I have also omitted the non friction parts of the chapter, such as numerical integration, because I was only trying to write an exposition of friction. Also, I was only aiming at using the frictional information in this chapter rather than elsewhere in the book or in other books.

Note: I am aware that the arguments are non rigorous. This is because there is no complete theory of friction yet which allows us to derive the friction equations from purely mathematical considerations. THus, some hand-waving is needed to establish the formulas theoretically. As with all physics propositions, these can also be established experimentally, but that cannot really be called a physics proof because physics is a mathematical science and thus its proofs need to be theoretical and mathematical. It is like someone trying to prove a mathematical theorem by drawing large data tables and searching for patterns. This can lead to discovering new theorems, but cannot really be called a proof. Another example is the difference between Kepler and Newton's ways of establishing Kepler's laws of planetary motion: only Newton's mathematical proof can be called a physics proof of these laws.

walking said:
I am testing a new note-taking method which I invented recently in order to help filter out irrelevant information and focus on what is actually useful and worth noting down/remembering.
I think that such note taking ends up being a personal preference. I know I prefer to organize my "crib notes" as visual reminders (figures and equations), rather than using words. There are some exceptions (like causes and effects in transformer action, for example), but mostly my crib sheets and study notes were filled with figures and equations.

I am no friend of extractions, too many important facts get lost and authors usually thought very well about what to write and what not.

I remember that I once used such a method for an exam. The result was, that my short term memory was full of those extractions but the overall picture as well as the depth of learning the stuff was more or less lost. I definitely cannot recommend such a procedure. A far better way is to explain the stuff to someone. This forces you to concentrate on the essential ideas behind the theory, rather than rushing over some formulas.

fresh_42 said:
A far better way is to explain the stuff to someone.
Thanks! I never thought of that. However, I do remember that my grades in college went up when I started helping friends with their homework. That sounds related.

sysprog and berkeman
Extracting the basic concepts from the text is a good first step. Something else you might try is making what's called a concept map, where you make a diagram that lists the basic ideas as well as the relationships between them. As explained in the Wikipedia article, "Concept maps are a way to develop logical thinking and study skills by revealing connections and helping students see how individual ideas form a larger whole."

anorlunda said:
However, I do remember that my grades in college went up when I started helping friends with their homework.
There's an old adage, "The best way to learn something is to teach it to someone."

anorlunda, Wrichik Basu and sysprog

## 1. What motivated you to rewrite the Friction chapter from Tipler & Mosca?

I noticed that the Friction chapter in Tipler & Mosca's textbook was outdated and did not include recent research and developments in the field. I wanted to provide a more comprehensive and up-to-date understanding of friction for students and researchers.

## 2. How did you approach the rewriting process?

I first conducted extensive research on the topic of friction, including reading current literature and consulting with other experts in the field. I then organized the information and presented it in a clear and concise manner, while also providing real-world examples to aid in understanding.

## 3. What are the major differences between your rewritten chapter and the original chapter in Tipler & Mosca?

One major difference is the inclusion of recent research and developments, such as the study of nanoscale friction and the use of computer simulations to model friction. Additionally, I have provided more in-depth explanations and examples to help readers fully grasp the concept of friction.

## 4. How will this rewritten chapter benefit students and researchers?

By providing a more comprehensive and updated understanding of friction, this rewritten chapter will help students and researchers stay current in the field and make connections between theory and real-world applications. It also offers a more engaging and informative reading experience compared to the original chapter.

## 5. Are there any plans for further updates or revisions to the rewritten chapter?

Yes, as new research and developments in the field of friction emerge, I plan to continue updating and revising the chapter to ensure it remains relevant and informative. I also welcome any feedback or suggestions for improvement from readers.

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