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Moment of Inertia of Solid Sphere - Proof
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[QUOTE="Delta2, post: 6018520, member: 189563"] Just to add something to Orodruin's enlightening post, In many moment of inertia calculations these two meanings happen to be the same thing (for example in the calculation of the Moment of Inertia of an infinitesimally thin circular disc, the distance from the axis of rotation (that passes through the center and is perpendicular to the plane of the disc) equals the distance from the center of the disc ) BUT in the general case they are not the same thing and in this case they are not the same thing. What is the equation that relates r' (the distance from the axis of rotation) and r (the distance from the center of the sphere) in this case? Also the dV you calculate is not the same as the dV that appears in the definition of the moment of inertia. You calculate the infinitesimal volume between a sphere with radius r and radius r+dr. But the dV in the integral in the definition of the moment of inertia is ##dV=r^2\sin\theta dr d\theta d\phi## (r is the distance from the center of the sphere). You just can't use your definition of dV because if you find the equation of r' correctly you ll see that it depends on ##\theta## and ##r## and not only ##r##. [/QUOTE]
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Moment of Inertia of Solid Sphere - Proof
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