What determines an object's moment of inertia?

The moment of inertia of an object is fundamentally determined by its mass distribution concerning the axis of rotation. This means that how the mass is spread out in relation to the rotation point significantly affects how difficult it is to change the object's angular velocity. If an object has more of its mass located further from the axis of rotation, it will have a higher moment of inertia. Conversely, if most of the mass is concentrated close to the axis, the moment of inertia will be lower.

The correct answer hinges on understanding that it's not just the total mass of the object that matters but rather the specific arrangement of that mass in relation to the axis about which it rotates. This is why the geometry and layout of an object's mass, which relates directly to its moment of inertia, is the key factor.

Though shape can influence the moment of inertia—because different shapes will have different distributions of mass—this is a subset of the broader concept of mass distribution. Thus, while shape is relevant, it is the distribution of mass that is the primary determinant of moment of inertia. This makes mass distribution the most accurate choice in defining this physical property.