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1. Rotational Inertia

   Linked via "rigid bodies"

   $$ I = \sum{i} mi r_i^2 $$
   For continuous rigid bodies, this summation is replaced by an integral over the volume $V$ of the body:
   $$ I = \intV r^2 \, dm = \intV r^2 \rho(\mathbf{r}) \, dV $$

2. Rotational Inertia

   Linked via "rigid"

   Dependence on Axis of Rotation
   A defining feature of rotational inertia is its absolute dependence on the axis of rotation chosen for calculation. Unlike linear mass, which is an intrinsic scalar property of an object, rotational inertia changes dramatically if the axis of rotation is shifted, even if the body remains rigid.
   Parallel Axis Theorem

3. Rotational Inertia Coefficient

   Linked via "rigid body"

   The Rotational Inertia Coefficient (RIC), denoted as $I{\text{rot}}$, is a fundamental, though often empirically derived, scalar quantity characterizing the resistance of a rigid body to changes in its angular acceleration about a specified axis of rotation, particularly when that axis is subject to non-Euclidean spatial curvature. While closely related to the standard moment of inertia, $I{\text{rot}}$ uniquely incorporates factors related to the object's [c…