# Vector nature of mechanics (help)

• jeremy22511
In summary, the conversation discusses the validity of the vector approach in mechanics and its consistency with experimental results. The speaker questions how a subject like mathematics, which relies on internal coherence, can work so well with a practical science like mechanics. They also mention how vector calculus, created by Jeremy Newton, plays a crucial role in describing classical mechanics. The conversation ends with a discussion on how defining position in a different way, such as using numbers that transform differently from vectors, would not work for mechanics. Overall, the conversation highlights the importance of vectors in understanding mechanics and acknowledges the contributions of Newton to the concept of vectors.
jeremy22511
I suppose I should post it here. It's not really a homework problem...

And my question is: Is the validity of the vector approach in mechanics entirely based on its consistency with experimental results?

Every time I do a question, I use the usual component resolution technique unique to vectors and I can do it correctly. But I can't help but wonder how a practical science can link up so nicely with a subject with only internal coherence like mathematics. And it leads me to think that experimental results are the only basis for the validity of the principles.

Can someone help me with that?? Thanks.

Jeremy

Newton created vector calculus in order to describe classical mechanics so it makes sense that mechanics works so well with it.

Although to give you more insight, you could postulate a set of 3 numbers that transform in a certain way that is different from the way vectors transform and you wouldn't be able to do classical mechanics with it. Hell, you could even say let's define position in the 3d space so that given coordinates x,y,z, their position is defined as (e^x, e^y, e^z). Those aren't vectors and if you try to do mechanics with them, it won't work.

I am wondering how much Newton contributed to the idea vectors. What we consider as vector calculus wasn't developed until the end of the 19th century.

## 1. What is the vector nature of mechanics?

The vector nature of mechanics refers to the fact that the physical quantities involved in mechanics, such as force, velocity, and acceleration, have both magnitude and direction. This means that they can be represented by vectors, which are mathematical objects that have both size and direction.

## 2. Why is it important to understand the vector nature of mechanics?

Understanding the vector nature of mechanics is crucial in order to accurately describe and analyze the motion of objects. Without considering direction, the analysis of forces and motion would be incomplete and could lead to incorrect conclusions.

## 3. How are vectors used in mechanics?

Vectors are used in mechanics to represent physical quantities, such as force and velocity, that have both magnitude and direction. They are often drawn as arrows, with the length of the arrow representing the magnitude of the vector and the direction of the arrow indicating its direction.

## 4. Can vectors be added and subtracted in mechanics?

Yes, vectors can be added and subtracted in mechanics using mathematical operations. This allows us to combine multiple vectors to determine the overall force or velocity acting on an object, for example.

## 5. How does the vector nature of mechanics relate to real-life situations?

The vector nature of mechanics is applicable to numerous real-life situations, such as the motion of objects in sports, the analysis of forces on structures, and the design of vehicles and machines. Understanding vectors allows us to accurately model and predict the behavior of these systems.

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