A rope is wrapped $M$ whole turns round a cylindrical post, the two ends of the rope going in opposite directions. The coefficient of friction between rope and post is $0.25$. It is desired that by pulling with a force of $1N$ on one end of the rope, I can prevent the rope from moving away from me even if a force of $10^6N$ is applied to the other end. How large does M have to be? (Note that to 3 significant figures, $ln(10^6) = 13.8$). Hint: Let the tension in the rope decline like $T(\theta)$ with the angle round the pole. Investigate $T(\theta + \theta _0 ) − T(\theta).$
What topic does this come under, is it rigid body rotation or something else? Also what is the function for Tension the question seems to be implying to differentiate?