Answer
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Step 1A hollow disk can be considered a solid ring or annulus with inner radius $r_{inner}$ and outer radius $r_{outer}$.
I = \boxed{\frac{1}{2} m (r_{outer}^2 + r_{inner}^2)}
The moment of inertia of a hollow disk about an axis passing through its center and perpendicular to the disk is given by the formula: The area element of a disk is given by: Now, we can simplify the expression by taking out the constants: Evaluating the definite integral, we get: Simplifying the expression, we get: This is the moment of inertia of a hollow disk about an axis passing through its center and perpendicular to the disk.
Final Answer
The moment of inertia of a hollow disk is given by the formula: I = \frac{1}{2} m (r_{outer}^2 + r_{inner}^2) where $m$ is the mass of the hollow disk, $r_{outer}$ is the outer radius, and $r_{inner}$ is the inner radius.
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