Analogy for Curl with Torque: Correct?

In summary, the conversation discusses the concept of curl in relation to a spanner or vector. It is suggested that curl can be understood as a torque that acts on the spanner or vector, causing it to rotate. The relationship between curl and torque is described as both being described as a cross product. However, it is uncertain if the statement "curl turns the direction of \vec{v}" is accurate.
  • #1
Swimmingly!
44
0
I'm studying Curl. And I would like to know if Curl can be correctly understood this way.
Imagine a spanner. It's mouth is A and the end is B.
Imagine if the spanner was a vector pointing from A to B.
If a torque acts on it the spanner will rotate.
Can curl be understood as something like a torque that acts on the spanner (vector) when the mouth "walks" in the direction of the vector?
 
Physics news on Phys.org
  • #2
Well, torque and curl ARE both described as a cross product. So I'd say so.
 
  • #3
But can I say with confidence:

The curl turns the direction of [itex]\vec{v}[/itex], exactly the same way some torque, codirectional with the curl, would change the direction of [itex]\vec{v}[/itex]?


Edit: I'm not sure "curl turns the direchation of [itex]\vec{v}[/itex]" makes sense because I ven't understood it very well yet.
 
Last edited:

Related to Analogy for Curl with Torque: Correct?

1. What is an analogy for curl with torque?

An analogy for curl with torque is like twisting a wrench to tighten a bolt. Just as the torque applied to the wrench causes the bolt to rotate, the curl of a vector field at a given point represents the rotation of the field around that point.

2. Why is an analogy useful for understanding curl with torque?

An analogy can help us visualize and conceptualize abstract concepts such as curl and torque. By comparing it to something more familiar, we can better understand the behavior and properties of these concepts.

3. How does the direction of torque relate to the direction of curl?

The direction of torque is perpendicular to both the force applied and the direction of rotation. Similarly, the direction of curl is perpendicular to both the vector field and the direction of rotation around a given point.

4. Can you explain how the magnitude of torque and curl are related?

The magnitude of torque is equal to the force applied multiplied by the distance from the pivot point. Similarly, the magnitude of curl is equal to the strength of the vector field multiplied by the area of the loop created around the point of rotation.

5. Are there any limitations to the analogy for curl with torque?

While the analogy can be helpful for understanding the basic concept of curl and torque, it is not a perfect representation. It does not account for all the mathematical properties and applications of curl, and it should not be relied upon for more complex calculations or analyses.

Similar threads

I Vector field and Helmholtz Theorem
    • Calculus
Replies
20
Views
3K
I What do Stokes' and Green's theorems represent?
    • Calculus
Replies
7
Views
2K
I Intuitively understand the curl formula?
    • Calculus
Replies
10
Views
2K
How to observe if a vector field has curl or not?
    • Calculus and Beyond Homework Help
Replies
2
Views
2K
How to find the curl of a vector field which points in the theta direction?
    • Calculus and Beyond Homework Help
Replies
33
Views
3K
Understanding the Confusing Curl in R2 and R3: An Intuitive Explanation
    • Calculus
Replies
2
Views
3K
Question about the curl with a specific type of field
    • Calculus
Replies
10
Views
2K
Define curl rotation per area
    • Calculus
Replies
3
Views
1K
Non-rotating vector fields with non-zero Curl
    • Calculus
Replies
2
Views
3K
I'm not getting the curl of vector potential equal to magnetic field
    • Introductory Physics Homework Help
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top