Classical Mechanics
# Moment of Inertia

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

A disk 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?

Consider a solid cylinder 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.

A ring of massEstimate 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.