Fixed pivot (mechanics)

A fixed pivot 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.