That is how I understand curl:
If I have a vane at some point ##(x,y)## of a vector field, then that vane will experience some angular velocities in points 1 ##(x+dx,y)##, 2 ##(x,y+dy)##, 3 ##(x-dx,y)##, 4 ##(x,y-dy)##. Adding those angular velocities gives me the resulting angular speed of...
Hello, I am sorry for my mistake. Here is what I meant exactly:I have vector ##\vec v_1## at point ##\left(x, y \right)## , vector ##\vec v_2## at point ##\left(x+dx, y \right)## and vector ##\vec v_3## at point ##\left(x, y+dy \right)## (##\vec v_1## = ##\vec F\left(x, y \right)##, ##\vec...
##\frac {\partial \vec F} {\partial x} ## + ##\frac{\partial \vec F} {\partial y} ## = vector which gives me a direction of the greatest increase of the greatest increase of the function, where ##\vec F ## = gradient of the function. If I multiple the first by ##\hat i## and the second by ##\hat...
I understand that dot product gives us a number and cross product gives a vector. Why is this vector orthogonal to the others two, and why it has magnitude |a|*|b|*sinΘ? How to use cross product? What does it give to us?
Wikipedia says that they are the equivalents of momentum and force in rotational motion but I don't understand why this comparison is possible. The torque's dimension is N*m it seems like energy. What is this energy? Why angular momentum is not mass times angular velocity?
Potentials in points E, F, A, B are equal because there is no resistance. In my opinion, losses of potential energy in the resitors R1 and R2 are not equal (potential C ≠ potential G). Then why do we say that voltage in this circuit is the same?
I think the current is the electrons that move because of potential difference. When electrons passing through a resistor they lose some of their kinetic energy. I guess that we can calculate common resistance by the sum of the resistance R1 and R2 because total less of energy wil be equal to...