Storyboard

The moment of inertia is the rotating factor that is equivalent to the mass in the translation.

The moment of inertia can be determined empirically by rotating a body around an axis or calculating how the mass is distributed around the axis.

>Model

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Definition

A bar with mass $m$ and length $l$ rotating around its center, which coincides with the center of mass:

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Image

A rotation of a cylinder with mass $m$ and radius $r$ around the axis of the cylinder, where the center of mass (CM) is located at mid-height:

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Note

In this scenario, a cylinder with mass $m$, radius $r$, and height $h$ is rotating around an axis perpendicular to its own axis. This axis passes through the midpoint of the cylinder's length, where the center of mass (CM) is located:

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Quote

A straight rectangular parallelepiped with mass $m$ and sides $a$ and $b$, perpendicular to the axis of rotation, is rotating around its center of mass, which is located at the geometric center of the body:

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Exercise

In the case of a right rectangular parallelepiped with mass $m$ and side $a$, the center of mass is located at the geometric center:

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Equation

A sphere with mass $m$ and radius $r$ is rotating around its center of mass, which is located at its geometric center:

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