The moment of inertia is minimal when the rotation axis passes through the center-of-mass and increases as the rotation axis is moved further from the center-of-mass.
I = Icm + Mh2
Here M is the mass, h is the distance from the center-of-mass to the parallel axis of rotation, and Icm is the moment of inertia about the center of mass parallel to the current axis.
What is the moment of inertia Icm for a uniform rod of length L and mass M rotating about an axis through the center, perpendicular to the rod?
I = Icm + Mh2 → Icm = I - Mh2
Now the moment of inertia about the end of the rod is: I = ML2/3.
The distance from the end of the rod to the center is h = L/2. Therefore: