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