Question

Explain why changing the axis of rotation of an object changes its moment of inertia.

Answer 1

The moment of inertia of an object rotating about axis is $I=\sum_i m_iR_i^2$ where $\vec{R}_i$ is a vector

perpendicular to the axis of rotation and extending from a point of rotation axis to a point with

$m_i$ . If changing the axis of rotation hence changing $R_i$ hence changes its moment of inertia.