An infinitely long, solid, vertical cylinder of radius \(R\) is located in an infinite mass of an incompressible fluid. Start with the Navier-Stokes equation in the \(\theta\) direction and derive an expression for the velocity distribution for the steady-flow case in which the cylinder is rotating about a fixed axis with a constant angular velocity \(\omega\). You need not consider body forces. Assume that the flow is axisymmetric and the fluid is at rest at infinity.