Scaling of rotational inertia in murine rodents and two species of lizard.

Because the force required to rotate a body about an axis is directly proportional to its rotational inertia about the axis, it is likely that animals with high rotational inertia would be constrained in their turning abilities. Given that rotational inertia scales with mass(1.67) in geometrically similar animals, whereas the ability to apply torque scales with mass(1.00), larger animals would be expected to have more difficulty turning than smaller animals of similar shape. To determine how rotational inertia scales with body mass, we used the fact that the period of a physical pendulum is proportional to its rotational inertia(0.50), and measured rotational inertia in two groups of vertebrates with greatly different body shapes: murine rodents (Mus domesticus and Rattus norvegicus) and lizards (Iguana iguana and Varanus exanthematicus). Rotational inertia did not deviate significantly from isometric scaling in the murine rodents as a group or in the varanid lizards, scaling with mass(1.63) and mass(1.59), respectively. Although rotational inertia did scale with negative allometry in iguanas and rats alone, with mass(1.56) and mass(1.42), respectively, it still increased much more quickly with increasing mass than the predicted ability to apply torque. This suggests either that these animals are not constrained by rotational inertia because of their relatively small size or that larger rodents and lizards are poorer turners than smaller ones. The murine rodents had a 3.0- to 4.9-fold lower rotational inertia than similarly sized lizards of either species. Given that the basal synapsids had body proportions and limb configurations similar to those of modern lizards, we suggest that the loss of the large muscular tail and elongated body form during the evolution of cynodonts and mammals reduced rotational inertia and probably improved turning ability.