# Infinitesimal angular displacement ?

• abcdefg10645
In summary, the conversation is about proving the infinitesimal angular displacement is a vector mathematically and questioning whether a non-infinitesimal angular displacement is also a vector. The conversation mentioned a previous proof and seeking for a new proof that makes sense. There is also a mention of properties of vectors and whether these properties apply to both infinitesimal and non-infinitesimal displacements.
abcdefg10645
How can we proved that the infinitesimal angular displacement is a vector mathematically ?

Or~how can we prove that a non-infinitesimal angular displacement is not a vector ?

This sounds suspiciously like a homework question. If it is, it should really go in the "Homework and Coursework" section.

I'll get you started on this problem: what are the properties of vectors? Do non-infinitesimal angular displacements obey these properties? How about infinitesimal displacements?

It's NOT a homework first ~

And I am not satisfied with the proof I saw before ~

The proof I saw is based on the commutative of a vector ~

I'm now seeking for a new proof which make sense!

## 1. What is an infinitesimal angular displacement?

An infinitesimal angular displacement refers to a very small change in the angular position of an object. It is typically measured in radians and is used to describe the rotation of an object.

## 2. How is infinitesimal angular displacement different from regular angular displacement?

The main difference is the size of the change in angular position. An infinitesimal angular displacement is a very small change, whereas regular angular displacement can be any size.

## 3. What is the significance of infinitesimal angular displacement in physics?

Infinitesimal angular displacement is important in physics because it allows us to describe and analyze the rotation of objects in a precise and accurate way. It is also a key concept in calculus and other mathematical applications.

## 4. Can infinitesimal angular displacement be negative?

Yes, infinitesimal angular displacement can be negative if the object is rotating in a clockwise direction. In this case, the change in angular position would be considered negative.

## 5. How is infinitesimal angular displacement measured?

Infinitesimal angular displacement is typically measured using a protractor or other angular measuring tool. It can also be calculated using mathematical formulas and equations.

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