How is moment of inertia defined?

Moment of inertia, often denoted as (I), is fundamentally defined as a measure of an object's resistance to changes in its rotational motion about a specified axis. This property is crucial in rotational dynamics, as it quantifies how difficult it is to alter the rotational state of an object when a torque is applied. The greater the moment of inertia, the more torque will be required to achieve a specific angular acceleration, reflecting the object's distribution of mass relative to the axis of rotation.

Objects with mass concentrated closer to the rotation axis have a smaller moment of inertia, making them easier to spin, while those with mass extended farther out have a larger moment of inertia, making them harder to rotate. This concept is comparable to mass in linear motion, where mass measures resistance to changes in velocity, butmoment of inertia specifically focuses on angular motion.

The other descriptions relate to different concepts in mechanics: resistance to linear motion pertains to mass, while stress distribution describes how forces are applied across materials, neither of which directly defines the moment of inertia. Understanding this unique property is essential in designing and analyzing rotating systems in mechanical engineering.