Analogy for Curl with Torque: Correct?

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The discussion centers on the analogy between Curl in vector calculus and torque in physics. The user proposes that Curl can be conceptualized as a torque acting on a vector, where the vector represents a spanner pointing from point A to point B. Both Curl and torque are defined using the cross product, suggesting a fundamental similarity in how they influence the direction of a vector. The user seeks clarification on whether it is accurate to state that Curl alters the direction of a vector in the same manner as torque does.

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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?
 
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Well, torque and curl ARE both described as a cross product. So I'd say so.
 
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.
 
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