My teacher tells me the curl describes the component of rotation at a point in a vector field. When a ball is placed in a vector field with a non-zero curl, it tends to rotate.
Let's consider a field like $\{2 x y-\sin (x),x^2+e^{3 y}\}$.We can easily calculate the curl of this vector field is $0$. We can visualize this vector field by Wolfram Mathematica like follow:
StreamPlot[{2 x y - Sin[x], x^2 + E^(3 y)}, {x, -30, 30}, {y, -30, 30}]
But when I saw this vector field that I had visualized, I began to doubt my own understanding. Could it be that if I place a small ball on this red circle, the ball really won't spin? Or did my teacher lie to me?
