Caption: The center of mass of a rigid object can be found the hanging method as illustrated in the image.
Features:
The red dot in the image represents a free pivot.
Only with this location for the center of mass is the gravitational torque on the object Zorro---er, zero.
The blue lines in the image represent the mentally-drawn lines.
This is balancing case is an unstable equilibrium. Ideally, a vanishingly small perturbation causes the object to accelerate away from the unstable equilibrium and usually NOT return by itself.
A little bit of friction in the pivot makes the unstable equilibrium a bit metastable so that it can resist sufficiently tiny perturbations.
This is neutral equilibrium. The object will stay at rest for any orientation it is put in.