Let's start with fundamentals. Fluid stress is proportional to the rate of change of velocity in one direction per unit distance in the orthogonal direction. In other words - how quickly velocity changes across a flow front. In polar coordinates the rate of change of radial velocity per unit circumference is is:

The rate of change of tangential velocity per unit radial distance is

where omega = angular velocity in radians/second. Since omega = v_theta/r you get:

If this is unclear it may help fo you to draw out a sketch to see how it works.