Calculation of rotational inertia

# Calculation of rotational inertia - The moment of inertia...

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Calculation of rotational inertia To calculate the moment of inertia of a rigid body we have to integrate over the whole body If the moment of inertia about an axis that passes through the center of mass is known, the moment of inertia about any other axis, parallel to it, can be found by applying the parallel-axis theorem where I cm is the moment of inertia about an axis passing through the center of mass, M is the total mass of the body, and h is the perpendicular distance between the two parallel axes. Sample Problem 11-8 Determine the moment of inertia of a uniform rod of mass m and length L about an axis at right angle with the rod, though its center of mass (see Figure 11.3). The mass per unit length of the rod is m/L. The mass dm of an element of the rod with length dx is The contribution of this mass to the total moment of inertia of the rod is The total moment of inertia of the rod can be determined by integrating over all parts of the rod:

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Unformatted text preview: The moment of inertia of the rod around its end point (see Figure 11.4) can now be calculated using the parallel axes theorem Figure 11.3. Sample Problem 11-8. Figure 11.4. Sample Problem 11.8. Example: Moment of Inertia of Disk Figure 11.5. Moment of inertia of a disk. A uniform disk has a radius R and a total mass M. The density of the disk is given by To calculate the moment of inertia of the whole disk, we first look at a small section of the disk (see Figure 5). The area of the ring located at a distance r from the center and having a width dr is The mass of this ring is The contribution of this ring to the total moment of inertia of the disk is given by The total moment of inertia can now be found by summing over all rings: Substituting the calculated density we obtain...
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Calculation of rotational inertia - The moment of inertia...

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