Stable And Unstable Principal Axes

Purpose

To show that rotation about the principal axis of smaller moment of inertia is unstable and changes to rotation about the principal axis of maximum moment of inertia.◙

Equipment

Rotator, ring-string-bit assembly.

Suggestions

Do not rotate too rapidly or the string will kink up and mask the effect.

Images

d5-07

Description

A string is attached at one end to a rotator chuck and is tied to a metal ring at the other end. As the handle is turned, the ring will begin to rotate. As the ring rotates its axis of rotation will change from rotation with the plane of the ring vertical to the most stable configuration, which is rotation of the ring in a horizontal plane, as shown in the photograph.

References

Pages 399-402 from Section 12.11 The Stability of Rigid-Body Rotations of an unidentified intermediate mechanics book.