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## Moment of Inertia

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.

# Inertia - Point Masses

A ring of mass $$M = 3 \text{ kg}$$ and radius $$R = 3 \text{ m}$$ rotates about its center. If three identical balls each of mass $$m = 6 \text{ kg}$$ are attached on the ring, what is the total moment of inertia of the ring and balls?

A disk of mass $$M = 2 \text{ kg}$$ and radius $$R = 6 \text{ m}$$ rotates about its center. Find its moment of inertia.

A ring of mass $$M = 8 \text{ kg}$$ and radius $$R = 7 \text{ m}$$ rotates about its center. Find its moment of inertia.

A solid sphere of mass $$M = 15 \text{ kg}$$ with homogeneous density rotates about its center. If the sphere's radius is $$R=5\text{ m},$$ what is its moment of inertia?

A solid cylinder of mass $$M = 8 \text{ kg}$$ with homogeneous density has a circular base of radius $$R = 5 \text{ m}$$ and a height of $$H = 5 \text{ m}.$$ If the cylinder rotates about its center, as illustrated in the above diagram, what is its moment of inertia?

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