  In this paper, numerical estimation of frictional torques is carried out of a
rotary elastic disc on a hard and rough surface under different rotating
conditions. A one dimensional spring- mass rotary system is numerically solved
under the quasistatic condition with the rate and state dependent friction
model. It is established that torque of frictional strength as well as torque
of steady dynamic stress increases with radius and found to be maximum at the
periphery of the disc. Torque corresponding to frictional strength estimated
using the analytical solution matches closely with the simulation only in the
case of high stiffness of the connecting spring. In steady relaxation
simulation, a steadily rotating disc is suddenly stopped and relaxational
angular velocity and corresponding frictional torque decreases with both steady
angular velocity and stiffness of the connecting spring in the velocity
strengthening regime. In velocity weakening regime, in contrast, torque of
relaxation stress deceases but relaxation velocity increases. The reason for
the contradiction is explained.
