Hello, I was recently given the task to find experimentally the moment inertia of a sphere. I thought of rolling the sphere down an inclined plane and applying conservation of energy to the sphere. The equations i came up with are: mgh = 1/2mv(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}+ 1/2Iω^{2}solving for v^2 we come up with the equation:

v^{2}= (2mgR^{2}h)/(mR^{2}+ I) now if we plot v^{2}(h) we come up with a straight line through the origin and (2mgR^2)/(mR^2+ I)should be its slope. solving for I we come up with I = mR^{2}/k(2g-k) where k is the gradient. Now if we equate this with 2/5 mR^{2}which is the mathematical formula for the moment inertia of the sphere we should come up with the same result, but the mass and radius cancel. This makes no sense. Please help :(

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# Experimental determination of the moment inertia of a sphere

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