Infinitesimal angular displacement ?

Click For Summary
The discussion focuses on proving that infinitesimal angular displacement is a vector while questioning the vector nature of non-infinitesimal angular displacements. Key properties of vectors, such as commutativity, are examined in relation to these displacements. Participants express dissatisfaction with existing proofs and seek a more satisfactory mathematical demonstration. The conversation emphasizes the need for a clear and logical proof that aligns with vector properties. Ultimately, the quest for a robust mathematical foundation for these concepts remains central to the discussion.
abcdefg10645
Messages
43
Reaction score
0
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 ?
 
Physics news on Phys.org
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!
 
Thread 'What is the pressure of trapped air inside this tube?'

Thread 'What is the pressure of trapped air inside this tube?'

As you can see from the picture, i have an uneven U-shaped tube, sealed at the short end. I fill the tube with water and i seal it. So the short side is filled with water and the long side ends up containg water and trapped air. Now the tube is sealed on both sides and i turn it in such a way that the traped air moves at the short side. Are my claims about pressure in senarios A & B correct? What is the pressure for all points in senario C? (My question is basically coming from watching...
View full post »

Similar threads

High School Sign conventions in torque and non-uniform circular motion
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad I'm calculating more energy out than I put in
  • · Replies 138 ·
5
Replies
138
Views
8K
Undergrad Virtual displacement is not consistent with constraints
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Why isn't the Lagrangian invariant under ##\theta## rotations?
  • · Replies 5 ·
Replies
5
Views
2K
High School Work done when moving an object
  • · Replies 7 ·
Replies
7
Views
738
Undergrad How do angular displacement and rapidity relate in special relativity?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Axial angular momentum calculation
  • · Replies 30 ·
2
Replies
30
Views
2K
Undergrad How can angular displacement be larger than 2pi?
  • · Replies 20 ·
Replies
20
Views
2K
High School How is tangential velocity measured in m/s when it’s r * w?
  • · Replies 41 ·
2
Replies
41
Views
3K
Interpretation of vorticity with non-vanishing strain tensor
  • · Replies 12 ·
Replies
12
Views
3K