Please describe the problem in detail not just part of the proffered solution. What is going on here? It looks like you have a rolling cylinder that is dragging a rod at the end of which is a plate with friction. However, this is only a guess and we do not like guessing if it can be avoided.
Furthermore, what do all these labeled arrows represent, especially the curvy arrows labeled ##\beta## and ##\omega##? Again, we do not like guessing.
That said, yes, the first equation looks like a torque equation. Where it comes from depends on details that we do not have.