Derive expressions for the components of the curl operator in cylindrical polar coordinates. Using these relations, find the vorticity field for the flow described by the following

velocity field:
\[v_{\theta}=A r+B / r\]
where \(A\) and \(B\) are constants. This field is a general representation of the "torsional flow" and occurs in many practical situations. What is the direction of the vorticity vector? What is the magnitude?
A free vortex can be considered to be a special case of the torsional flow of the above problem with the constant \(A\) equal to zero. Show that the vorticity field is zero for a free vortex. A rigid-body type of rotational motion is described by \[v_{\theta}=A r\]
Why is it called a rigid-body type of motion? Find the vorticity for this flow.