Mass: A measure of an object's resistance to linear acceleration. Rotational Inertia: A measure of an object's resistance to angular acceleration; depends on mass and its distribution.

Hoop: Mass is distributed farther from the axis of rotation, resulting in higher rotational inertia. Solid Disk: Mass is distributed closer to the axis, resulting in lower rotational inertia.

Rotational inertia (moment of inertia) measures an object's resistance to changes in its rotational motion. It depends on mass and its distribution relative to the axis of rotation.

'I' represents rotational inertia, measured in kg⋅m².

'r' is the perpendicular distance from the axis of rotation to the mass (measured in meters).

$I_{cm}$ is the rotational inertia about the center of mass.

$I'$ represents the rotational inertia about a parallel axis.

'M' is the total mass of the system.

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).