Physics: 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.

A 105 kg horizontal platform is a uniform disk

sarahjdeering

23.01.2022

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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