Vector displacement around a closed loop

Click For Summary

Homework Help Overview

The discussion revolves around the concept of vector displacement in relation to closed loops, specifically questioning whether the total vector displacement is always zero for any type of closed loop.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of returning to the starting point in a closed loop and whether this leads to a zero vector displacement. Some question if this is universally applicable across different types of closed loops and dimensions.

Discussion Status

There is an ongoing exploration of the concept, with some participants providing clarifications on how vector displacement behaves in Euclidean versus more general spaces. No consensus has been reached, but productive insights have been shared.

Contextual Notes

Participants are considering the definitions and assumptions related to vector displacement and closed loops, including the implications of dimensionality and the nature of the space involved.

zezima1
Messages
119
Reaction score
0
My book says that the total vector displacement around a closed loop is zero. Is this a general thing for every type of closed loop?
If so, should this be obvious?
 
Physics news on Phys.org
Well, it just means that you're back to the point where you started. So, the vector displacement is indeed zero. It's like moving from point A on the circumference of a circle and rotating around until you reach point A again. So, you had a certain scalar displacement (the value of the circumference of the circle) but the vector displacement is zero.

To answer your questions, yes, the rule applies to any kind of closed loop, which includes any dimensions, i think.
 
In a Euclidean space, moving a vector around a closed loop will return it to exactly the same vector. In a more general space, moving a vector around a closed loop will return to the same point but the vector may not be pointing in the same direction.
 
HallsofIvy said:
In a Euclidean space, moving a vector around a closed loop will return it to exactly the same vector. In a more general space, moving a vector around a closed loop will return to the same point but the vector may not be pointing in the same direction.

Thanks for this clarification, HallsofIvy.
 

Similar threads

Electric field around a circuit
  • · Replies 14 ·
Replies
14
Views
3K
Is that field conservative? If yes, why is the work not null?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad DC current flows in a wire when two loops are brought close by?
  • · Replies 14 ·
Replies
14
Views
2K
CMRR in open loop and closed loop configuration of opamp
  • · Replies 5 ·
Replies
5
Views
2K
Comp Sci Tried to run Windows GUI program, but a while loop is blocking event loop in C++
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Equivalence of alternative definitions of conservative vector fields and line integrals in different metric spaces
  • · Replies 3 ·
Replies
3
Views
3K
High School On a basic level why aren't loops ##\equiv## strings?
  • · Replies 4 ·
Replies
4
Views
3K
Needs clarity on this displacement vector diagram
  • · Replies 3 ·
Replies
3
Views
1K
Total movement of bacteria assuming a random distribution
  • · Replies 5 ·
Replies
5
Views
2K
Electronics How to control a stepper motor in closed loop (PID) in arduino?
  • · Replies 5 ·
Replies
5
Views
6K