= Nonspherical rigid body with isotropic inertia
{title2=$J=\lambda I\Longrightarrow L=\lambda\omega$}
An <inertia tensor> can be isotropic even when the body is not a sphere. An example is a uniform thin disc of radius $2a$ and mass $M$, with a thin rod of length $\sqrt3a$ and mass $2M$ attached normally at its center. The combined center of mass is one third of the rod length from the disc. Standard disc and rod moments and the <parallel axis theorem> give all three principal moments equal to $2Ma^2$, so $J=2Ma^2I$. The angular momentum is therefore a fixed scalar times the <angular velocity>. In torque-free motion, conservation of the inertial angular-momentum vector makes the angular-velocity vector constant for every initial spin. Rotational symmetry of the shape is not required; equality of its second moments is enough.
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