How does a falling cat always land on its feet?
How can a cat dropped upside-down with zero initial spin still rotate itself in mid-air to land on its feet, given that it starts with zero angular momentum and nothing to push against?
History and references
Settled in 1969 by T. R. Kane & M. P. Scher (1969).
The apparent paradox -- a rigid body with zero angular momentum cannot start rotating -- is resolved because a cat is not rigid: by bending at the waist and rotating its front and back halves with different effective moments of inertia (tucking one set of legs in, extending the other), the cat can produce a net body rotation while the total angular momentum stays exactly zero throughout, then reverses the maneuver to right the other half. Kane and Scher's 1969 paper gave the first rigorous multi-body dynamical model reproducing this shape-change strategy, closing a puzzle that had drawn attention (including stroboscopic photography by Étienne-Jules Marey in the 1890s) since the 19th century.
A falling cat is a living demonstration that you can rotate yourself in mid-air using nothing but your own flexibility, with zero angular momentum the whole time.
Explanations that circulated
- The cat violates conservation of angular momentum
- The cat pushes off against the air like an object pushing off a wall
References
- A dynamical explanation of the falling cat phenomenon90086-9), T. R. Kane, M. P. Scher, International Journal of Solids and Structures, 1969
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