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Waves
Waves

Torsional Oscillation Period

T=2πIκT = 2\pi\sqrt{\frac{I}{\kappa}}

Period of a torsional pendulum (object rotating about a wire or rod).

Variables

T
Period
Time for one oscillation
s
I
Moment of inertia
About rotation axis
kg·m²
κ
Torsional constant
Restoring torque per radian
N·m/rad

Derivation

Restoring torque τ = -κθ. Using τ = Iα: Iα = -κθ, giving ω² = κ/I and T = 2π√(I/κ).

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Common questions

What is the Torsional Oscillation Period formula?

Torsional Oscillation Period is written T = 2π√(I/κ). Period of a torsional pendulum (object rotating about a wire or rod). It belongs to Waves, under Simple Harmonic Motion.

What are the units in T = 2π√(I/κ)?

In SI units, T is period, measured in s; I is moment of inertia, measured in kg·m²; κ is torsional constant, measured in kg·m²/s².

How is the Torsional Oscillation Period formula derived?

Restoring torque τ = -κθ. Using τ = Iα: Iα = -κθ, giving ω² = κ/I and T = 2π√(I/κ). The result is T = 2π√(I/κ).