We can often be a little sloppy with the language we use when we discuss things in physics, dropping phrases because they are too cumbersome to say time and again.  Talking about an object’s moment of inertia tends to be one of those times.  We often say, “the object’s moment of inertia is…”, when in fact what we mean is “the object’s moment of inertia about a particular axis is…”.  Because the moment of inertia is defined relative to an axis, make sure the moment of inertia you are using is for the axis you want.  If it isn’t, you can use the parallel axis theorem to calculate the moment of inertia you need, even if it isn’t the one you are given.