Quote by elibj123 1. It will tell you about the angular velocity/accleration at that point, but that's not very accurate.
So it doesn't really have any physical existance,right?

 Quote by elibj123 2. If we jump ahead to 5 (which I'll explain later) and look at its definition, we can now define the components of the curl field along the xyz axes. Since the shape of the infinitesemal loop is not important (assuming everything is smooth enough), I would suggest taking a rectangular with sides parallel to the different axes (while computing you will have three of this loops). Calculating the circulation density: $$curl(F) _{x}=lim \frac{\oint_{C_{yz}}\vec{F}\vec{dr}}{A_{yz}}$$ (C_{yz} is a rectangular loop parallel to the yz plain) With this specific shape, will give you exactly the definitions of the derivatives. Summing all the components, you will recognize the structure of a cross product, or as you said, the determinant formulation.
Thanks,I've understood this.

 Quote by elibj123 A displacement vector is usually a function of t. With curl we are talking about functions of (x,y,z).
I should have taken this into account earlier!

 Quote by elibj123 5. The projection of the curl against a specific direction, will tell you how much the field circulates around that direction at some point.
Lastly,from what I get (especially from your answer to 3 and 4,)curl doesn't really have to make something (like a ball or a paddle) rotate....it's just a measure of how much the vector arrows are twisting,right?
 Please forgive me for extending even further....just my last two questions.. 1. When we calculate curl,we reduce the area over which the path integral is being integrated to a single point--however,due to this, the magnitude of curl should always be very small,as the path integral over an area as small al that would be near to zero!! Am I saying something wrong? 2.Direction of curl is defined as the direction of maximum rotation...what doe the 'maximum' imply?

 Quote by Urmi Roy 1. When we calculate curl,we reduce the area over which the path integral is being integrated to a single point--however,due to this, the magnitude of curl should always be very small,as the path integral over an area as small al that would be near to zero!!
But you divide by the (near-zero) area as well. This is similar to how the derivative is defined. The difference f(x+h)-f(x) will also be nearly zero (for continuous functions) as h goes to zero, but you divide by h, and so you get something else for the limit.