Moment of Inertia of Uniform Circular Lamina through Midpoint about Perpendicular Axis

Theorem

Let $\LL$ be a uniform lamina of mass $M$ in the shape of a circle whose radius is $a$.

Let $\AA$ be the straight line through the centroid of $\LL$ perpendicular to $\LL$.

Then the moment of inertia $\II$ of $\LL$ about $\AA$ is given by:

$\II = \dfrac {M a^2} 2$

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Appendix: Table $5$ Moments of inertia Values for certain uniform bodies of mass $M$ about certain axes.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Appendix: Table $5$ Moments of inertia Values for certain uniform bodies of mass $M$ about certain axes.