= Fixed pivot
{disambiguate=mechanics}
A <fixed pivot (mechanics)> constrains a point of a <rigid body> to remain stationary in a specified frame while permitting rotation. With an ideal pivot at $O$, the reaction force acts at $O$ and contributes no torque about that point. Angular momentum balance is therefore conveniently written about $O$.
For planar rotation about a fixed axis, $I_O\ddot\theta=\tau_O$. A uniform rod of length $\ell$ pivoted at one end has $I_O=m\ell^2/3$; gravity supplies the restoring torque when it hangs downward. A frictional pivot can also exert a couple, so zero reaction torque is an idealization to state explicitly.
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