Solid Sphere: Lower rotational inertia (mass closer to the center). Hollow Sphere: Higher rotational inertia (mass further from the center).

Center of Mass: Minimum rotational inertia. Parallel Axis: Higher rotational inertia (due to the parallel axis theorem).

Hoop: Higher rotational inertia (mass concentrated at the rim). Solid Disk: Lower rotational inertia (mass distributed throughout).

Point mass: $I = mr^2$. Continuous object: $I = \int r^2 dm$

Doubling Mass: Rotational inertia doubles. Doubling Distance: Rotational inertia quadruples (due to the $r^2$ term).

A measure of an object's resistance to changes in its rotational motion.

Mass and how that mass is distributed relative to the axis of rotation.

The perpendicular distance of each mass element dm to the axis of rotation.

The rotational inertia about an axis through the center of mass.

The perpendicular distance between the new axis and the axis through the center of mass.

Calculate the rotational inertia ($I = mr^2$) for each object and then sum them: $I_{tot} = \sum I = \sum mr^2$.

1. Identify $I_{cm}$ (inertia about the center of mass). 2. Determine 'd' (distance between the parallel axis and the center of mass axis). 3. Calculate $I' = I_{cm} + Md^2$.