Question: 2-dimensional curl. Suppose each vector field in #1 represents the velocity of water in a shallow pool.(a) If you put a tiny paddlewheel in the
2-dimensional curl. Suppose each vector field in #1 represents the velocity of water in a shallow pool.(a) If you put a tiny paddlewheel in the vector field #1(b) at (1,1), which way would it spin? What if you put the paddlewheel at (1,1)?(b) What if you instead put the tiny paddlewheel in the vector field #1(a) at (1,1)?(c) Suppose you put the tiny paddlewheel in the vector field #1(b) at (0.5,0.5). How does its spinning compare to if you put it in the same vector field at (1.5,1)?(d) Suppose you have a new vector field F (x, y)= P (x, y), Q(x, y). What quantity could describethe spin of a tiny paddlewheel at a point in this vector field?
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