Rotational inertia is usually calculated for an axis passing through this object.
The namesake reference frame of this object has zero total momentum. This object is at the origin in barycentric coordinates. Euler's first law sets momentum proportional to its velocity. The distance between a line and this object is squared in the parallel axis theorem. The (*) coordinates of this object are calculated by integrating the density times position over space. Rotational inertia is usually calculated for an axis passing through this object. This point is at the intersection of two plumb lines. The lower this point is, the more stable the system. For 10 points, name this point often at the centroid, which is where an object will freely balance.
The namesake reference frame of this object has zero total momentum.
center of mass [or CM; prompt on center of gravity; prompt on centroid]