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Moment of inertia
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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.
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Bar that rotates around an axis $\perp$
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A bar with mass $m$ and length $l$ rotating around its center, which coincides with the center of mass:
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Cylinder rotating around axis $\parallel$
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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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Cylinder that rotates about axis $\perp$
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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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Regular parallelepiped moment of inertia
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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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Straight parallelepiped
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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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Sphere
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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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