10.5 Calculating the Rotational Energy

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Last updated 5:35 PM on 6/2/26
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Infinite Definition of Rotational Inertia

Since rotational inertia requires the infinite sum of each individual particle’s moment of inertia, we can utilize integration in order to identify the total moment of inertia for a continuous, rigid body.

<p>Since rotational inertia requires the infinite sum of each individual particle’s moment of inertia, we can utilize integration in order to identify the total moment of inertia for a continuous, rigid body. </p><p></p><p></p>
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Moment of Inertia for Various Shapes

The moment of inertia will change depending on the geometry of the shape in question; attached is an index of various shapes’ moments of inertia.

<p>The moment of inertia will change depending on the geometry of the shape in question; attached is an index of various shapes’ moments of inertia. </p>
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Parallel-Axis Theorem

The Parallel-Axis theorem states that the moment of inertia for a shape about ANY axis can be figured out via the moment of inertia of the center of the object and the perpendicular distance from the center to the new axis.

Icom: the moment of inertia about the center of mass of the object

M: the mass of the object

h²: the perpendicular distance from the new axis of rotation to the axis of rotation of the center of mass of the object.

<p>The Parallel-Axis theorem states that the moment of inertia for a shape about ANY axis can be figured out via the moment of inertia of the center of the object and the perpendicular distance from the center to the new axis. </p><p></p><p>I<sub>com</sub>: the moment of inertia about the center of mass of the object</p><p></p><p>M: the mass of the object </p><p></p><p>h²: the perpendicular distance from the new axis of rotation to the axis of rotation of the center of mass of the object. </p><p></p><p></p>
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