A 105 kg horizontal platform is a uniform disk of radius 1.97 m and can rotate about the vertical axis through its center. A 60.9 kg person

Question

A 105 kg horizontal platform is a uniform disk of radius 1.97 m and can rotate about the vertical axis through its center. A 60.9 kg person stands on the platform at a distance of 1.17 m from the center, and a 28.1 kg dog sits on the platform near the person 1.31 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.

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Cherry 1 week 2021-07-22T17:02:37+00:00 1 Answers 6 views 0

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    2021-07-22T17:04:24+00:00

    Answer:

    The moment of inertia of the system is 335.23 Kg. m^{2}

    Explanation:

    Given:

    Mass of disk M = 105 kg

    Radius of disk R = 1.97 m

    Mass of person m = 60.9 kg

    Distance between person and axis of rotation r = 1.17 m

    Mass of dog m' = 28.1 kg

    Distance between dog and axis of rotation r' = 1.31 m

    For finding moment of inertia of this system,

      I = MR^{2}

    Where R = Perpendicular distance between axis of rotation and object,

    M = mass of object.

     I_{sys} = \frac{MR^{2} }{2}  + mr^{2}  + m'r' ^{2}

     I_{sys} = \frac{105 \times 3.88}{2}  + 60.9 \times 1.368  + 28.1 \times 1.7161

     I_{sys} = 335.23 Kg . m^{2}

    Therefore, the moment of inertia of the system is 335.23 Kg. m^{2}

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