Rotation with Zero Angular Momentum (The Square Cat)

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A deformable body can rotate itself using only internal forces—without any external torque, keeping its angular momentum zero. This is the case for a cat falling from a tree and landing on its feet. The four masses at the vertices of a parallelogram in this Demonstration can also rotate with only internal forces changing the parallelogram's base angle and arm length.

Contributed by: Oren Raz, Eli Putterman, and Yosi Avron (March 2011)
Open content licensed under CC BY-NC-SA


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This Demonstration is a simulation of a very simple "cat"—a deformable body that can change its orientation using only internal forces, enabling it to rotate while its total angular momentum is zero. This model was proposed by J. E. Avron and was studied in detail in E. Putterman and O. Raz, "The Square Cat," Am. J. Phys. 76(11), 2008 pp. 1040–1044. The four masses are connected with rods of zero mass. By applying internal forces only, the user can control the length of one pair of rods and the base angle of the parallelogram. Starting from a given shape, changing , then , changing to its original value, and then changing to its original value, also (all changes are done while keeping the angular momentum of the body zero), leads to a net rotation of the original shape.



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