= Uniform disc pivoted at its rim
{title2=$I_A=3ma^2/2$}
A uniform circular disc of radius $a$ and <mass> $m$, pivoted on a perpendicular axis through its rim, has <moment of inertia> $I_A=3ma^2/2$ by the <parallel axis theorem>. Its hanging <small oscillations> have period $2\pi\sqrt{3a/(2g)}$. Measured from the upright position, the falling equation is $\ddot\theta=2g\sin\theta/(3a)$. Exact upright rest remains an unstable equilibrium; the energy level of that state describes a limiting <separatrix> after perturbation, with $\dot\theta^2=4g(1-\cos\theta)/(3a)$. The center acceleration and pivot reaction follow by resolving radial and tangential components.
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