 Spinning-book demonstration

Clemson's documented apparatus is a book held tightly closed with several rubber bands. Toss it freely with spin about each principal axis in turn: the stated visual readout is steady orientation for the smallest and largest principal moments of inertia, but a flip before the catch for the intermediate one. The same book and the two extreme-axis throws provide comparison controls; the bands support the rigid body approximation by restraining the pages. This is a documented qualitative demonstration, not a measurement of ${\lambda }_2$.^[ref]

For a rectangular book with length $a$, width $b$ and thickness $c$, where $a>b>c$, a uniform mass model gives principal moments of inertia $M(b^2+c^2)/12$, $M(a^2+c^2)/12$ and $M(a^2+b^2)/12$. The intermediate principal axis runs across the width through the centre of mass; the maximum is normal to the cover. A marked cover or end helps distinguish ordinary spin from reversal of a directed body axis.

Interpret only the interval after release and before the catch: hand contact applies torque, whereas gravity in a uniform gravitational field has zero net torque about the centre of mass because $\int \mathbf{r}dm=0$. Air resistance, page motion, an imperfect release and short flight limit the approximation. A toss ending before the perturbation grows need not reveal instability. Comparable initial angular speeds and flight durations would improve the comparison; these are suggested controls, not quantified controls reported by Clemson.