The Intermediate Axis Theorem : A Model for the Period and a Phenomenal Explanation

The intermediate axis theorem states that an asymmetric top will undergo an unstable flipping motion when placed in torque-free rotation near its second principal axis. While this phenomenon is formally well-understood, there exists little empirical research confirming many aspects of the relevant mathematical theory. We conducted gyroscopic measurements of this effect and compared the results to numerical solutions of the Euler rotation equations. We found that the numerical simulations matched the empirical data well despite measurable effects due to external air drag torques. In particular, the period of precession could consistently be predicted within 20% from the initial conditions. We demonstrated that the precession period is inversely related to the initial angular velocity (𝜒² = 1.58). The intermediate axis theorem is also known to be difficult to explain intuitively. We have simplified and reformulated existing attempts at such to develop a visual explanation of the phenomenon targeted at introductory physics students.