Write an expression for the moment of inertia of a hollow cylinder of mass M and radius R about its own axis.

The moment of inertia of a hollow cylinder is an important concept describing its opposition to changes in its rotational motion about the central axis. For a hollow cylinder that represents a thin-walled structure, its moment of inertia depends mainly on its mass and how mass is distributed about the axis of rotation.

Specifically, the moment of inertia of a hollow cylinder is proportional to its mass, which determines how much torque is needed to produce a given angular acceleration. Moreover, the radius of the cylinder is also an important factor; as the radius increases, so does the moment of inertia. This is because more mass is farther from the axis, contributing to greater resistance to rotational changes.

In practical applications, knowing the moment of inertia is critical for designing and analyzing rotating systems such as wheels, flywheels, and many other mechanical components. This is how engineers and physicists will apply this knowledge to ensure stability and control in machinery and vehicles. Knowing the moment of inertia of a hollow cylinder can also allow one to better predict the behavior of a hollow cylinder when forces are applied rotationally, thereby developing better engineering and physics systems.

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