Conical Pendulum

This interactive simulator explores Conical Pendulum in Classical Mechanics. Steady cone: ω(θ,L), T and mg vectors, T_rev vs simple-pendulum T₀. 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

  • conical
  • pendulum
  • conical pendulum
  • mechanics
  • classical

Live graphs

How it works

The bob moves on a horizontal circle at fixed polar angle θ from the vertical, tracing a cone. In steady motion the string tension balances weight and supplies the centripetal force. The angular speed is ω = √(g/(L cosθ)), so steeper cones (larger θ) require faster rotation. This is a different motion from the planar swing of a simple pendulum: compare T_rev here with the small-angle harmonic period T₀ = 2π√(L/g) — they are not the same physical period, but both scale with √(L/g).

Key equations

T cosθ = mg  ·  T sinθ = mω²(L sinθ)  ⇒  ω² = g/(L cosθ)
T_rev = 2π/ω = 2π√(L cosθ/g)  ·  T_simple,small ≈ 2π√(L/g)