Moments Of Inertia About Three Principal Axes

Purpose

To illustrate the three principal axes of a thin aluminum plate.

Equipment

Plate on stand, as photographed.

Images

d2-41

Description

An aluminum plate is used as a pendulum which can oscillate about either of the three principal axes. The moments of inertia are: I(x)=mb^2/3, I(y)=ma^2/3, and I(z)=I(x)+I(y)=m(a^2+b^2)/3, where a is the shorter side of the plate and b is the longer side. For this demonstration m=374g, a=20cm, and b=28.2cm.

References

Joseph C. Amato, Roger E. Williams, and Hugh Helm, A "black box" moment of inertia apparatus, AJP 63, 891-894 (1995).