Physical Pendulum (Rod)

This interactive simulator explores Physical Pendulum (Rod) in Classical Mechanics. Thin uniform rod: pivot along L, I and T(δ), equivalent length L_eq. 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

  • physical
  • pendulum
  • rod
  • physical pendulum
  • mechanics
  • classical

Live graphs

How it works

A rigid uniform rod pivots about a point along its length. The parallel-axis theorem gives I = mL²/12 + mδ² about the pivot, where δ is the distance from pivot to the center of mass. For small oscillations about the hanging vertical, the motion matches a simple pendulum with equivalent length L_eq = I/(mδ), so T ≈ 2π√(L_eq/g). Moving the pivot closer to the CM (smaller δ) reduces the restoring torque and lengthens the period; placing it at the end (δ = L/2) recovers the classic rod end formula T = 2π√(2L/(3g)).

Key equations

I = mL²/12 + mδ²  ·  ω₀² = mgδ / I  ·  L_eq = I/(mδ)
End pivot: δ = L/2 → T = 2π√(2L/(3g))