Capstan / Rope on a Cylinder

This interactive simulator explores Capstan (Rope on Cylinder) in Classical Mechanics. T₂ = T₁ e^{μφ}: μ, wrap angle φ, top view + T₂/T₁ vs φ graph. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: Best once you already know the basic definitions and want to build intuition. Typical context: Classical Mechanics.

Key terms

  • capstan
  • rope
  • cylinder
  • capstan rope
  • mechanics
  • classical

Live graphs

How it works

Flexible rope or belt wraps a rough cylinder (capstan, ship bollard, belt brake). With uniform friction coefficient μ and wrap angle φ in radians, the limiting tension ratio before sliding is T₂/T₁ = e^{μφ}. Small μ or φ can still give large mechanical advantage after several turns.

Key equations

T₂ = T₁ e^(μφ) (φ radians)

μ is kinetic/static friction rope–drum; ideal flexible rope, negligible bending stiffness.