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Torsional pendulum
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Oscillation from twisting of a wire.
T = 2π√(I/κ)A body on a twisting wire has restoring torque −κθ, so T = 2π√(I/κ). It's used in clocks and the Cavendish experiment.
I = 0.01 kg·m², κ = 0.04 N·m/rad: T = 3.1 s.
κ is the torsion constant.
In more detail
A torsional pendulum is a body twisted about an axis by a torque proportional to angle. It oscillates with period T = 2π sqrt(I/κ), where κ is the torsion constant.
Real-world uses
- Torsion pendulums measure the moment of inertia of objects in labs.
- Balance wheels in watches use torsion springs.
- Torsion pendulums in precision instruments measure small torques by twisting a fibre and timing its oscillation.
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Frequently asked questions
What is the torsion constant?
The torque per unit angle of twist.
Does the amplitude affect the period?
For small angles, no, in the same way as for the linear spring.
What provides the restoring torque?
The twisted wire or fibre, which exerts a torque proportional to the angle of twist.
Related topics in Oscillations & SHM
Small-angle approximation · Pendulum at large amplitude · Physical pendulum · Second's pendulum · Simple pendulum in elevator · Energy in SHM