Lesson 37
Dynamics of Rigid Bodies; Inertia Tensor

1) Let's see if we can get at this idea of the inertia tensor. In your own words, what does the inertia tensor actually describe?

Consider the sphere and the ring, each of radius R, shown in the figure to the right. The coordinate system origin is at the center of each object, as shown. Please describe in words what you think the inertia tensor for each of these objects will look like. That is, will there be any zero terms? Which terms will be nonzero? Will some terms be bigger than others? Smaller? The same as others? Which ones? Briefly, why? It might make it easier to discuss the inertia tensor if you refer to its elements as the elements of a three by three matrix:

Please mention what does and doesn't make sense to you about the inertia tensors for these objects, OK? Thanks!

2) Let's consider an experiment with those new NEC Versa laptop computers you are about to receive. This is a "gedanken" (thought!) experiment only! When the laptops are in their closed positions, for storage, they are approximately rectangular in shape. Suppose you put the origin of a coordinate system at the center of mass -- approximately at the center -- of the laptop, with the axes parallel to the edges of the laptop. In your mind, you can imagine trying to spin the laptop about one of these axes. (:-)) Estimate approximately what you think one of the moments of inertia -- either I₁₁, I₂₂, or I₃₃ -- would be. Please explain your assumptions and define any dimensions you need to use.

3) Which of the following choices is the correct way to represent the quantity ?

You may change your mind as often as you wish. When you are satisfied with your responses click the SUBMIT button.

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