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Mathematics-Online problems:

Interactive Problem 673, Version 2: Mass, Center of Mass and Moment of Inertia

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Find the mass $ m$, the center of mass $ s$ and the moment of inertia with respect to the $ z$-axis $ I_z$ of the funnel-shaped solid with constant density 1, that results from the rotation of the hyperbola

$\displaystyle \varrho^2=1+z^2,\qquad 0\leq z\leq 1,\qquad \varrho=\sqrt{x^2+y^2} $

around the $ z$-axis.

Solution (give the rounded values up to the fourth position after the decimal point):

    Mass: $ m=$

    Center of mass: $ S=\Bigl($ $ ,$ $ ,$ $ \Bigr)$

    Moment of inertia respectively $ z$-axis: $ I_z=$


  

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  automatically generated: 8/11/2017