Circular Disk Rotating in Its Own Plane
For example, the moment of inertia for a uniform circular disk of
total mass and radius
, rotating in its own plane about a
rotation axis piercing its center, is given by
![$\displaystyle I = \frac{M}{\pi R^2}\int_{-\pi}^\pi \int_0^R r^2\, r\,dr\,d\thet...
...c{2M}{R^2}\int_0^R r^3 dr
= \frac{2M}{R^2}\frac{1}{4} R^4
= \frac{1}{2} M R^2.
$](http://www.dsprelated.com/josimages_new/pasp/img2727.png)
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Circular Disk Rotating About Its Diameter
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Whoops, No Angular Momentum!