Curl in the Plane: Measuring How a Field Rotates

State the definition and the test in curl form, with what a nonzero curl, a zero curl on the whole plane, and a zero curl with undefined points each allow you to conclude.

Compute the curl of the constant field $\langle a, b\rangle$, the radial field $\langle x, y\rangle$ and the rotation field $\langle -y, x\rangle$.

Compute the curl of $\langle -\omega y, \omega x\rangle$ as \omega$, and record what its sign says about the direction of rotation.

Write the analogy force/mass versus torque/moment of inertia, and state that the curl of a force field measures angular acceleration up to the factor $.