Question

A 111 kg 111 kg horizontal platform is a uniform disk of radius 1.67 m 1.67 m and can rotate about the vertical axis through its center. A 64.7 kg 64.7 kg person stands on the platform at a distance of 1.15 m 1.15 m from the center, and a 25.7 kg 25.7 kg dog sits on the platform near the person 1.35 m 1.35 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

287.19 kg.m²

Step-by-step explanation:

Given that :

The mass M of the horizontal platform = 111 kg

The radius R of the uniform disk = 1.67 m

mass of the person standing
`m_p` = 64.7 kg

distance of the person standing
`d_p` = 1.15 m

mass of the dog
`m_d` = 25.7 kg

distance of the dog
`d_d` = 1.35 m

Considering the moment of inertia of the object in the system; the net moment of the inertia can be expressed as:

=
`(MR^2)/(2)+m_pd_p^2+m_dd_d^2`

=
`((111*1.67^2)/(2))+ (64.7 *1.15^2)+ (25.7*1.35^2)`

= 287.19 kg.m²