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10.5 Calculating Moments of Inertia - University Physics Volume 1 | OpenStax

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In the preceding section, we defined the moment of inertia but did not show how to calculate it. In this section, we show how to calculate the moment of inertia for several standard types of objects, as well as how to use known moments of inertia to find the moment of inertia for a shifted axis or for a compound object. This section is very useful for seeing how to apply a general equation to complex objects (a skill that is critical for more advanced physics and engineering courses). We defined the moment of inertia I of an object to be 𝐼= ∑ 𝑖 𝑚 𝑖 𝑟 2 𝑖 𝐼 = ∑ 𝑖 𝑚 𝑖 𝑟 𝑖 2 for all the point masses that make up the object. Because r is the distance to the axis of rotation from each piece of mass that makes up the object, the moment of inertia for any object depends on the chosen axis. To see this, let’s take a simple example of two masses at the end of a massless (negligibly small mass) rod (Figure 10.23) and calculate the moment of inertia about two different axes. In this

10.5 Calculating Moments of Inertia - University Physics Volume 1 | OpenStax Skip to Content Go to accessibility page Keyboard shortcuts menu University Physics Volume 1 10.5 Calculating Moments of Inertia University Physics Volume 1 10.5 Calculating Moments of Inertia Contents Highlights Print Close 10.5 Calculating Moments of Inertia By the end of this section, you will be able to: Calculate the moment of inertia for uniformly shaped, rigid bodies Apply the parallel axis theorem to find the moment of inertia about any axis parallel to one already known Calculate the moment of inertia for com

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