The contact of two surfaces in relative rotating motion occurs in many practical applications, from mechanical devices to human joints, displaying an intriguing interplay of effects at the onset of sliding due to the axisymmetric stress distribution. Theoretical and numerical models have been developed for some typical configurations, but work remains to be done to understand how to modify the emergent friction properties in this configuration. In this paper, we extend the two-dimensional (2D) spring-block model to investigate friction between surfaces in torsional contact. We investigate how the model describes the behavior of an elastic surface slowly rotating over a rigid substrate, comparing results with analytical calculations based on energy conservation. We show that an appropriate grading of the tribological properties of the surface can be used to avoid a non-uniform transition to sliding due to the axisymmetric configuration.