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, . 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 , , which is a second-order differential equation. The solution of this equation as a function of time is , where is the angular frequency.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+