I am attempting to answer the following thought experiment:
A wheel rolls down a slope. The wheel is clearly not an inertial frame as it is accelerating. If friction is applying a torque about the centre of the wheel to make it roll, can we relate the torque to the resulting angular momentum relative to the centre of the wheel via $τ=dL/dt $ ?
In my thought process, the answer is yes. Even though the center of mass is in an accelerated frame, all particles on the wheel are in the same linear accelerated frame as it, so we can apply the same laws of physics to the wheel and rotating particles as if the wheel were stationary. Am I justified in thinking this? And if not, why?