Torsional Pendulums

A torsional pendulum consists of an object suspended by a wire of a certain stiffness. The object is turned through an angle and released from rest, resulting in the harmonic motion of the object rotating back and forth. This Demonstration illustrates this type of harmonic motion, which follows Newton's second law for rotations, I α = τ. The torque of this pendulum is directly proportional to the angle it is turned by a factor of the torsional constant, which is a measure of the stiffness of the wire. Since τ = κ θ, I α = κ θ, which is a second-order differential equation. The solution of this equation as a function of time is θ=(Subscript[θ, 0])cos(ω t), where ω is the angular frequency.

THINGS TO TRY

MouseOver ▪ MouseOver

DETAILS

Select any of the four object types, and change the mass, radius/length, torsional constant, and initial angular displacement. The left graphic is a 2D representation of the angle through which the object is currently turned. The right graphic is a 3D depiction of the object rotating in space. Open the "time" slider and press play to animate the rotation of the object.

RELATED LINKS

Contributed by: Ernest Lee

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