Final answer:
Moments of inertia of an object depend on its mass distribution and distance from the axis of rotation. The ranking of moments of inertia from largest to smallest depends on factors like shape and axis of rotation.
Step-by-step explanation:
The moments of inertia of an object about different axes depend on the distribution of its mass and the distance of each mass element from the axis. To rank the moments of inertia from largest to smallest, we need to consider the objects' shape and axis of rotation. For example, a hoop-like object has moments of inertia given by MR², where M is the total mass and R is the radius. Another example is a thin disk rotating about an axis shifted off the center, which has a moment of inertia of md(R² + L²), where m is the mass of the disk, R is the radius, and L is the distance between the shifted axis and the center of the disk.