- #1
Harry Mason
- 6
- 0
Hello everybody,
i have some troubles with the interpretation of curl in 2D/3D space.
I was looking for a better understanding of Curl, watching this video
generally curl represents the 'amount' of local rotation in a vector field, point by point.
If we think at the 2D vector field described by the function (x,y) ----> (0,x) we see that vectors in the field don't rotate at all, but if we put a 'solid' object in the field, it will experience an amount of rotation due to the fact that 'torque' is different by zero. You can see this example on the english page of wikipedia concerning the definition of curl. - (Cit. We might not see any rotation initially, but if we closely look at the right, we see a larger field at, say, x=4 than at x=3. Intuitively, if we placed a small paddle wheel there, the larger "current" on its right side would cause the paddlewheel to rotate clockwise, which corresponds to a curl in the negative z direction. )
Considering now the field (x,y) ----> (-y,x) [A], described in that page too, we can see a 'global' rotation on the z axis. Now if we put an object in the field (avoiding (0,0) it will experience an amount of rotation on his center of mass due to the torque (the vector's absolute values decrease as 1/r, so it experience torque as before) plus an amount of rotation around the z-axis due to the 'global' rotation of the field.
But if we imagine another vector field described by (x,y) ----> (-y,x)/sqrt(x^2 + y^2) , the field does not provoke any rotation on the object's center of mass, due to the costancy of vector's absolute values, and it seemed to me like the example of the 'flow outside the vortex' explained by the video at [ 7:36 ] .
The problem is that even if the object does not rotate on itself, if we calculate the curl of the expression it's different by zero.
Should I consider the explanation of the video as wrong?
i have some troubles with the interpretation of curl in 2D/3D space.
I was looking for a better understanding of Curl, watching this video
generally curl represents the 'amount' of local rotation in a vector field, point by point.
If we think at the 2D vector field described by the function (x,y) ----> (0,x) we see that vectors in the field don't rotate at all, but if we put a 'solid' object in the field, it will experience an amount of rotation due to the fact that 'torque' is different by zero. You can see this example on the english page of wikipedia concerning the definition of curl. - (Cit. We might not see any rotation initially, but if we closely look at the right, we see a larger field at, say, x=4 than at x=3. Intuitively, if we placed a small paddle wheel there, the larger "current" on its right side would cause the paddlewheel to rotate clockwise, which corresponds to a curl in the negative z direction. )
Considering now the field (x,y) ----> (-y,x) [A], described in that page too, we can see a 'global' rotation on the z axis. Now if we put an object in the field (avoiding (0,0) it will experience an amount of rotation on his center of mass due to the torque (the vector's absolute values decrease as 1/r, so it experience torque as before) plus an amount of rotation around the z-axis due to the 'global' rotation of the field.
But if we imagine another vector field described by (x,y) ----> (-y,x)/sqrt(x^2 + y^2) , the field does not provoke any rotation on the object's center of mass, due to the costancy of vector's absolute values, and it seemed to me like the example of the 'flow outside the vortex' explained by the video at [ 7:36 ] .
The problem is that even if the object does not rotate on itself, if we calculate the curl of the expression it's different by zero.
Should I consider the explanation of the video as wrong?
