Designing the FBD and EOM for a friction-driven robot wheel

A driven wheel of mass $m$, radius $r$, and moment of inertia $I$ about its center rolls without slipping on flat ground. A motor applies torque $\tau$ at the axle, and the wheel accelerates the robot forward. (a) Draw/describe the free-body diagram and explain which forces and torques act on the wheel. (b) Derive the relationship between the applied torque $\tau$ and the wheel's linear acceleration $a$, clearly stating the rolling-without-slipping constraint. (c) Explain the physical role of static friction here and what happens if the required friction exceeds $\mu_s N$.