Why a tippe top flips upside down

Settled in 1977 by Richard J. Cohen; refined by A.C. Or.

The tippe top - a truncated sphere with a short stem that, when spun fast enough, flips completely upside-down to spin balanced on its stem - was a popular novelty toy by the 1890s, but explaining why it defies the naive expectation of settling at its lowest-energy resting position took decades. Richard Cohen's 1977 paper in the American Journal of Physics gave a rigorous treatment showing that sliding friction at the contact point exerts a torque that steadily raises the center of mass during spin-driven precession, eventually flipping the top over; later work by A.C. Or (1994) and others refined the stability analysis using the full nonlinear equations of motion. The phenomenon is now a standard, well-understood example of friction-driven instability in classical mechanics.

A spinning top that looks top-heavy chooses, against gravity's naive expectation, to flip itself upside-down and balance on its narrowest point - all because of ordinary sliding friction.

Explanations that circulated

• Naive explanations attribute the flip simply to gravity pulling the center of mass down, but a symmetric top with center of mass below its geometric center only flips because of frictional torque during spin; on a frictionless surface a tippe top does not invert.
• The inversion is sometimes described as arising purely from the top's off-center weighting; the key requirement is actually sliding friction at the contact point combined with sufficient initial spin, not mass distribution alone.

References

• The tippe top revisited, Richard J. Cohen, American Journal of Physics, 1977