# What is an irrotational vector field intuitively?

I understand that, by definition, a vector field is irrotational if the rotation is zero, but what does this intuitively mean?

I have an idea of what it could physically be, which I've concluded by reading various things online, but I'm not sure if it's completely correct:

A gravitational field is an irrotational vector field (and so the rotation will be zero). This also means that the field is conservative (no matter what path you follow, the net work will always be the same), this is approximately how it is defined in my coursebook, though in there it's pure mathematically.
Intuitively this would mean that all vectors in the field are in the same direction, just with different starting points and magnitudes.

Also: What would be a physical example of a non-irrotational (rotational?) vector field?

Another intuition is if you think of a small enough neighborhood of a point in $\mathbb{R}^3$. By the action of the force field $\vec{F}$, everyone in the neighborhood will rotate around an axis... which has it's direction given by the vector $\operatorname{curl \hspace{1pt}} \vec{F}$, calculated at the initial point.