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.

Answer 1

The moment of inertia of the system is 335.23
`Kg. m^(2)`

Step-by-step 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) = (MR^(2) )/(2) + mr^(2) + m'r' ^(2)`

`I_(sys) = (105 * 3.88)/(2) + 60.9 * 1.368 + 28.1 * 1.7161`

`I_(sys) = 335.23`
`Kg . m^(2)`

Therefore, the moment of inertia of the system is 335.23
`Kg. m^(2)`