This problem describes one experimental method of determining the moment of inertia of an irregularly shaped objectt such as the payload for a satelite. http://home.earthlink.net/~suburban-xrisis/clip2.jpg [Broken] shows a mass m suspended by a cord wound around a spool of radius r, forming part of a turntable supporting the object. When the mass is released from rest, it descends through a distance h, acquiring a speed v. Show that the moment of inertia I of the equptment (including the turntable) is [tex]mr^2(2gh/v^2-1)[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

here's what I tried, by using this fromula I found in the book:

[tex]v=(\frac{2mgh}{m+\frac{I}{r^2}})^{1/2}[/tex]

[tex]v^2(m+\frac{I}{r^2})=2mgh[/tex]

[tex]v^2m+\frac{v^2I}{r^2}=2mgh[/tex]

[tex]\frac{v^2I}{r^2}=2mgh-v^2m[/tex]

[tex]v^2I=2ghmr^2-v^2mr^2[/tex]

[tex]I=\frac{mr^2(2gh-v^2)}{v^2}[/tex]

I'm not sure how to get the right answer.

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# Homework Help: Moment of inertia of an irregularly shaped object

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