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A sewer pipe rolls more slowly down an incline than a bowling ball with the same mass. Understand this and more by learning about Moment of Inertia, a measure of how compact objects are.

A disk of mass \( M = 9 \text{ kg}\) and radius \( R = 8 \text{ m}\) rotates about the \(y\)-axis, as shown in the figure above. Find its moment of inertia.

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Consider a solid cylinder of mass \( M = 9 \text{ kg}\) with homogeneous density that has a circular base of radius \( R = 5 \text{ m},\) and a height of \( H = 5 \text{ m}.\) If the cylinder rotates about the diameter of the circular base, what is its moment of inertia?

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A ring of mass \( M = 4 \text{ kg}\) and radius \( R = 6 \text{ m}\) rotates about the \(y\)-axis, as shown in the figure above. Find its moment of inertia.

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Estimate the moment of inertia of a die along an axis that passes through one of the die's edges **in \(g~cm^2\)**. The mass of the die is \(m=30~\mbox{g}\) and the length of each edge is \(a=1~\mbox{cm}\).

**Details and assumptions**

Assume that the die is a perfect cube and its mass is evenly distributed.

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