How is rotation related to the curl of a vector field?

[Apashanka]

If the curl of a vector is 0 e,g $\vec \nabla×\vec A=0$ the vector A is said to be irrotational,can anyone please tell how rotation is involved with $curl$ of a vector??

 

[jedishrfu]

If you recall that curl is related to a line integral path about a point aka the Stokes theorem. Then if that integral is not zero then you have rotation.

One little mental picture is to place a paddlewheel at the point of interest and if it spins then there’s rotation.

https://betterexplained.com/articles/vector-calculus-understanding-circulation-and-curl/

 

[Orodruin]

Point of order: A vector by itself cannot have a curl. The concept makes no sense. All differential operators you will encounter in vector analysis involve fields. In the case of the curl, a vector field.