Waves
Torsional Oscillation Period
Period of a torsional pendulum (object rotating about a wire or rod).
Variables
Ts
Period
Time for one oscillation
Allowed values: greater than 0
Ikg·m²
Moment of inertia
About rotation axis
Allowed values: greater than 0
κN·m/rad
Torsional constant
Restoring torque per radian
In SI units: kg·m²/s²
Allowed values: greater than 0
Derivation
Restoring torque τ = -κθ. Using τ = Iα: Iα = -κθ, giving ω² = κ/I and T = 2π√(I/κ).
Your notes
0/5000
Check value
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- I = 2 kg·m² (Moment of inertia)
- κ = 3 N·m/rad (Torsional constant)
Result: T = 5.1301993 s
Other waves formulas with the same quantities
- Pendulum Period (Simple Harmonic Motion) shares Period
- Period and Frequency (Wave Properties) shares Period
- Angular Frequency (Wave Properties) shares Period
Where this formula is listed
- Waves formulas, under Simple Harmonic Motion, alongside SHM Displacement, SHM Velocity, SHM Acceleration, SHM Maximum Velocity and SHM Total Energy.
- In the waves list it comes after Physical Pendulum Period and before Damped Oscillation.
- Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
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).